Of all the terrestrial meats commonly eaten, rabbit has the least fat, which isn't to say that it's non-existent. Any way that you cook chicken you can also cook rabbit.
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Is a chicken a "terrestrial meat"? I observe that martian meats, venusian meats, and Klingon Gaaakh! are not readily available at the local Piggley-Wiggley.
A chicken is a rather incompetent creature of the air.
The Spanish claim that paella should have meats from land (pork and sausage), sea (lobsters, shrimp, crawdads) and air (chicken), and it certainly is a tasty dish, but a chicken rarely takes to the air.