This is an absolutely wonderful story that Stephen Colbert tells about meeting his wife. It's wonderful not just for the story itself, but the vibrant way he tells it with great verve. It's impromptu, but comes across as if written by an eloquent writer. He's clearly told it before and honed to its fine-tuned charm, but it's still off the cuff -- the shorter version, as he puts it at the end.
This doesn't appear to be told during a broadcast, but before the show when coming to the stage to meet the audience beforehand.
And as long as we're on the subject, here's a bonus companion piece. When talking to guest Leslie Mann, Colbert spots his wife in the wings and briefly and adorably brings her onstage.