While they both mean "a small laugh", they are slightly different sounds. A chuckle is deeper and sounds more masculine. A giggle is higher-pitched and sounds more feminine.

To giggle and to chuckle is almost the same thing. However, a chuckle is more of a "hah-hah" kind of thing, while giggle is more of a "hee-hee".

I agree with Kimberly. They don't have to be gendered, but a "giggle" is more of a cute or high-pitched laugh (so it's more commonly associated with girls or children), and a "chuckle" is more of a quiet or low laugh, such as if someone is just slightly laughing about something (either because it's only a little bit funny, or because the person just doesn't have a strong reaction even when s/he is amused by something). I'd say the main difference is that a "giggle" is usually a bit silly. In a formal business meeting, you could "chuckle" at someone's joke, but it might be weird if you were to "giggle."