If you just happen to run into an old friend, you can say you chance upon them. You weren't planning to see them; it was a complete coincidence.
When you discover something, you chance upon it: "I was surprised to chance upon a place that serves cheese fondue." And when you accidentally meet someone, you chance upon that person: "Did you chance upon any other Americans on the cruise?" This verb is a slightly old fashioned way to say "run into" or "come across."