In order to answer this question, we need to start with chickens and work our way back through the evolutionary family tree.

Does chicken taste like chicken? Don’t laugh—this is an important question. Even lifelong chicken eaters usually have a very narrow experience because the birds sold in grocery stores are usually one of a very few breeds that have been designed to grow a lot of breast meat very quickly in factory-farm settings. A Plymouth roasting hen slaughtered for market at 7 weeks does not make for the same eating experience as a 2-year-old Rhode Island Red. I once ate a bantam rooster that tasted more like iguana than a grocery store chicken.

The most interesting paragraph was the explanation of why fish do not taste like chicken:

Several barriers prevent fish from tasting like chicken. A chemical called trimethylamine, which develops after a fish dies and creates that distinctly fishy flavor and odor, is a big one. Texture also plays a role: Fishes’ muscle structure is different from chickens’.  Fish muscles are typically arranged in bands along the sides of the body and are separated by relatively less connective tissue than what is found in the muscle of their evolutionary descendants. These bands of muscle are what make cooked fish flaky. Fish muscles are relatively simple because all they have to do to move through water is perform a sort of sideways flopping motion. The muscles of land-dwellers like chickens, lizards, and frogs are more specialized and are designed for the more varied movement of individual limbs.

The conclusion? About 350 million years ago is probably when life began to taste like chicken.