Alligators are actually quite vocal creatures that can make a wide variety of noises, including chirps, growls, bellows and hisses. Below is a video of hatching baby alligators in which they're making a sort of chirping sound to call to their mother. They do this so that big momma can come and help them out, uncovering the nest and possibly even carrying the babies to the water. Mother gator will protect them for quite some time, up to a year. If you don't want to watch the whole video, skip to 1:30.
The sound may be cute, but just remember: never pick up or mess with a wild animal! Even though baby alligators really can't hurt you very much, momma can, and if you hear that chirping noise it's likely she won't be far behind.
For contrast, here's a big male alligator bellowing for a mate. Watch how he makes the water dance!