The American Alligator (Alligator mississippiensis) is farmed commercially in the U.S. and enjoyed in as a Cajun delicacy in the South, especially Louisiana.
Why it hasn't made it very far outside of that region as a staple meat is anyone's guess, but maybe it's because it's often served fried and there are cheaper ways to fry up meat than using expensively farmed gator: hog rectum, anyone?