Whether or not you want to chew your oyster is totally up to you. Chewing your oysters will help you enjoy more of their natural flavor. Many people chew their steamed, grilled, or fried oysters, as they have a slightly different texture that is easy to chew. Chewing fried oysters is also the best way to take in all the flavor. Some people choose to swallow their raw oysters whole. While others prefer to chew their oysters whether they eat them raw or steamed.