Yes, and it's possibly the best time to start! "Mommy and Me" swim class when I was 18 months old meant that I learned to swim before conscious memory - I don't remember not knowing how to swim.

My mom was a great parent and wonderful overall, but that was a particularly excellent decision of hers. She was still careful with my little brother and me around water - we were enrolled in Red Cross swim classes during the summers in elementary school, and always had lifejackets on at the lake. Despite being terrible at pretty much all sports (unlike my athletically-gifted brother), I was always a decent swimmer.