Robert Donat is so completely believable as the 83-year-old man. Not only does he look different, but he carries himself completely different. He sounds completely different. When he delivers the somewhat teasing and grumpy old man line of, "Enough of your loathsome statistics woman, go about your business" you certainly can't imagine that coming from the younger version of himself. What a difference in demeanor and presence between the older Mr. Chips and the young, shy instructor who speaks slow and looks so awkward. I would have sworn on my life that they hired an old man to play the part. How on earth - in 1939 - did they make a 34-year-old Robert Donat look so different and believable as an 83-year-old?
I also want to mention Greer Garson's role too. It is amazing how skillfully and gracefully Katherine helps ease his uncomfortableness at social situations and teaches him how to interact with confidence. I think I have fallen for Greer Garson in this role. She is peaches and cream, delightful ... perfection.
This movie is a testament to storytelling. Chips isn't an extraordinary man really, he is someone that we can identify with - a shy person who learns to reach out. Give good actors and a good director a wonderful, simple story to tell without all of today's over-the-top trappings and this is what you often get - magic. I highly, highly recommend this one if you haven't already seen it.