Ahh, THAT is illegal here in the United States. Unless you own property and can get Tags from wildlife and fisheries. Or, have permission to hunt on certain properties and then the land owner must be consulted , in order to obtain tags. Each property is alloted a certain number of tags, so it's not like you can just go alligator hunting and kill whatever you want.
Additionally :
To apply, you must submit a completed alligator hunter license application form, proof of property ownership (tax receipts or bill of sale), a map of the property, and the landowner's signature indicating permission for the hunter to harvest alligators on the property.
If these requirements are not met, and you get caught , you will be facing a hefty fine, possible jail time, seizure of weapons used and revocation of hunting privileges for a sustained period of time.
Furthermore, you don't just go alligator hunting and shoot them where you see them. You bait a hook, or you will never see that Gator again.