During a break and on a walking tour of the Tyrolean Alps, Chips loses his way in the fog during a solitary climb on a snow-covered peak (A comment is made: "He hasn't climbed for years"). He flaps his arms to keep warm and frets: "This is a nice business. I could be here all night." And as he sits to light his pipe, he hears a woman from afar, crying: "Helloooooo." He is shocked, "Good heavens, a woman," but responds: "Helloo....Are you in danger?" He struggles with his walking cane in the direction of the voice, nearly falling down a precipitous rocky cliff, and then bumping into a cross bearing a sign for one of the craggy mountain's victims: "In Memory of One who lost his life here."

And then he meets a charming, beautiful, spunky English girl from Bloomsbury named Katherine Ellis (Greer Garson in her exceptional film debut) who appears behind the mist. She is calmly subdued and eating her lunch:

Katherine: Here I am. Hello there. I thought I heard a voice.
Chipping: Are you all right?
Katherine: Yes, quite thanks. The mist is a nuisance, isn't it?
Chipping: You're not in any danger?
Katherine: No. Do you mind?
Chipping: No, of course not but...
Katherine: You shouldn't be moving about, you know, it's very foolish of you.
Chipping: Foolish, but I heard you call. I thought you were in some difficulty.
Katherine: Don't tell me you climbed up here to rescue me.
Chipping: Well, as a matter of fact, I did.
Katherine: Oh, ha, ha, ha, now really, I should be very angry with you. Supposing you'd fallen.
Chipping: I must say I...
Katherine: I never heard of such utter stupidity. Where were you?...And you climbed up in that mist to rescue me when I'm probably a better climber than you are.
Chipping: Well, what were you screaming about?
Katherine: I wasn't screaming. I just let out a shout at random. I- so that was why. When I think that that road might have been paved with your good intentions. Really, it was idiotic of you - and rather wonderful.
Chipping: Not at all.
Katherine: Well anyway, I'm glad you came. It was gonna be very lonely.

They introduce themselves formally, and then share lunch in the clouds. She is amused by his old-fashioned-ness and his protective concern for her:

Katherine: I'm sorry I wasn't in any danger.
Chipping: It was rather inconsiderate of you. What are you doing alone on a mountain? Isn't it rather unusual for a young lady?
Katherine: I'm not usually alone. I have a friend at the inn.
Chipping: Oh, so have I. We're on a walking tour.
Katherine: Really? We're bicycling.
Chipping: Bicycling? Through Austria? Good heavens. I didn't know ladies rode those awful things.
Katherine: I'm afraid so.
Chipping: With one leg on each side of the saddle?
Katherine: Well, you don't imagine I ride side-saddle, do you?
Chipping: What happens to your dress?
Katherine: Oh, they breed female bicycles now, didn't you know?
Chipping: Ladies riding bicycles! I don't approve of all this rushing around on wheels. The other day, a man passed me in a cloud of dust. He must have been doing fifteen miles an hour. You know, human beings were never intended to go that speed. I suppose you think I'm old-fashioned?
Katherine: I like men to be old-fashioned.

Although he awkwardly protests, they share his jacket for warmth against the cold air. Down below the mountain, a search-party is being assembled by Max and Flora (Judith Furse), Katherine's companion. Higher up, he is exhilarated by her company in the altitude of the mountain air - she offers a penny for his thoughts, and he finds it amazing that she finds him "nice-looking" and "charming":

Katherine: A penny for your thoughts.
Chipping: As a matter of fact, I was thinking of you.
Katherine: Kindly, I hope.
Chipping: I see very little of ladies at Brookfield. I was rather realizing what I've missed.
Katherine: If I may say so, Mr. Chipping, I think the ladies have missed a great deal too.
Chipping: Oh, it's very kind of you, but I'm really not a ladies' man.
Katherine: Afraid of them?
Chipping: Terrified.
Katherine: (amused) Not of me, I hope.
Chipping: No, not up here in the clouds. Perhaps the altitude's gone to my head, but if I'd met you at the inn...
Katherine: 'Cause I'm a strong-minded female who rides a bicycle and wants the vote.
Chipping: No, no, no, on the contrary. Because...
Katherine: Because...?
Chipping: Well, because you're so very nice-looking I think and charming.
Katherine: So are you, Mr. Chipping, frankly.
Chipping: Good heavens, no one has ever called me that. (They both share a mutual laugh.) What extraordinary ideas come into one's head up here!
Katherine: It's the altitude.
Chipping: Do you experience a sort of exhilaration?
Katherine: Definitely.
Chipping: As though we owned the mountain.
Katherine: To put it mildly.
Chipping: We're pretty superior persons.
Katherine: We're gods.
Chipping: Up here, there's no time. No growing old. Nothing lost.
Katherine: We're young.
Chipping: We believe in ourselves.
Katherine: We have faith in the future.
Chipping: It must be the altitude.

Musing, he asks her if one can start life over again in middle age. She doesn't believe one can ever get old in a school - "in a world that's always young," full of young boys growing up. She inspires him to re-examine his life and profession:

Chipping: Do you suppose a person in middle age could start life over again and make a go of it?
Katherine: I'm sure of it. Quite sure. It must be tremendously interesting to be a schoolmaster.
Chipping: I thought so once.
Katherine: To watch boys grow up and help them along. To see their characters develop and what they become when they leave school and the world gets hold of them. I don't see how you could ever get old in a world that's always young.
Chipping: I never really thought of it that way. When you talk about it, you make it sound exciting and heroic.
Katherine: It is.
Chipping: (He turns to her) And the schoolmaster? Is he exciting and heroic too?
Katherine: (referring to him) I've met only one - a reckless person who climbed the Blochner in a mist...

When the foggy mist lifts, they reluctantly have to return 'back to reality' from their adventure: "And I'm almost sorry," Katherine comments. Upon their safe rescue, the vacationeers in the inn/chalet that evening raise a toast to the "hero of the mist" - the modest Mr. Chipping. Reacting shyly to the attention, the fuddy-duddy schoolmaster retires to his room early for the evening, avoiding a party in his honor.

Alone and unseen on the balcony later that night as he contently smokes his pipe, he overhears Katherine's rhapsodies about him (the 'knight errant') and the "thrilling" memories of their day on the mountain, as she speaks to Flora from their adjoining balcony. She defends him as being unlike an 'old stick-in-the-mud':

Flora: He might have been young and splendid looking. Then you'd have known you'd met your fate.
Katherine: He isn't at all old, darling, and I think he's quite charming.
Flora: Kathy!
Katherine: I mean it. He's just shy, Flora, and a little difficult to know perhaps. I'm sorry for shy people. They must be awfully lonely sometimes.

Max relays a message to Chipping following the evening's celebration - Katherine fears she may never see him again: "Miss Kathy asked me to say goodbye and to thank you again...They are going away early in the morning on their bicycles." During the remainder of their walking tour, Chipping thinks about the woman whom he met, hoping to be reunited with her: "That was a very intelligent young woman...I wonder if we might run into them again on our travels."

Both groups of tourists by chance are on a Danube River cruise bound for Vienna, chatting on different outer decks about the 'blue-ness' of the water - an indication from a legend that Chipping and Katherine are in love: "The Danube is only blue to the eyes of, uh, well, to people in love, you know." They meet as they disembark onto the dock: "We always seem to meet in a mist," and he escorts her down the gangplank. Both couples attend a ballroom dance wearing 'evening dress,' where Viennese waltzes played by a live orchestra serenade them. Flora and Max whirl away the evening together, as Katherine and Chipping sit and talk:

Katherine: Have you ever been in love, Mr. Chipping?
Chipping: No. Oh yes, yes I was once.
Katherine: I thought so.
Chipping: Rather a long time ago. I was fourteen at the time. She was the green grocer's daughter.
Katherine: And papa and mama intervened, I suppose.
Chipping: Yes, and so did the green grocer...Pitty this all has to end tomorrow.
Katherine: For us, but not for you. You have three weeks more.
Chipping: Oh yes, yes, that's true, but...
Katherine: (turning away shyly) It's been wonderful.
Chipping: For me, too. What will stand out in your memory?
Katherine: Oh, why I don't know...the music. What will you remember?
Chipping: I really can't say.
Katherine: Shall I tell you?
Chipping: Can you?
Katherine: The waltz you danced in Vienna.
Chipping: (questioning) The waltz I danced in - what, when?
Katherine: Tonight, now.
Chipping: (protesting) Oh but I couldn't possibly. I don't dance! Good heavens, I haven't danced since my college days.
Katherine: Are you turning me down?
Chipping: In front of all these people? Oh, no, no, no, really. It's quite out of the question.
Katherine: Well, of course it is, I'd really rather not. It would have been fun, just once before going home.
Chipping: (in a formal, hard-shelled manner) (standing) Miss Kathy, may I have the pleasure of this dance?
Katherine: I shall be happy, Mr. Chipping.

She encourages him for how "splendidly" he twirls her. As the night progresses, she has "solemn thoughts" about leaving: "I was thinking of tomorrow and railway stations - and goodbye." The next day as the women's bicycles are loaded onto their departing, crowded coach, they stutter their goodbyes and farewells to each other, contemplating how goodbyes are always awful. He breathlessly proposes marriage to her after their short, genteel and restrained courtship:

Chipping: I just wanted to say you made this the most wonderful holiday of my life and...you must go. Goodbye, Miss Kathy.
Katherine: (She shakes his hand.) Goodbye, Mr. Chips. (She kisses him directly on the lips and then boards the train.)
Chipping: (as the train pulls away) Miss Kathy! Kathy! Kathy! You, you kissed me!
Katherine: (leaning out the train window as he runs alongside) I know, it was dreadful of me.
Chipping: Oh no, no, but do you, are we, oh, this is awful. Here, you'll have to marry me now, you know.
Katherine: Do you want to?
Chipping: I do want to. Do you, too?
Katherine: Dreadfully.
Chipping: Oh!
Katherine: Goodbye, my dear.
Chipping: Kathy! (He reaches out) Oh, you can't go now, my dear.

After she waves back, he disconsolately speaks to Max: "She's gone. I don't know where she's gone. I may never see her again." His friend reassures the stunned, wide-eyed Chipping that Flora and he have already been planning the details of their wedding for days:

I shouldn't worry, Chipping. Miss Flora has selected the church already. And I'm to be best man. My good fellow, you imagine that we were both blind and deaf. We are going to open a bottle of champagne at the first cafe that we come to.