Yes, there is no article here for tavuk. However, tavuk is an object here and for it to mean "THE chicken", you need to use the accusative form of the noun (I think it is covered in a later lesson). When it is used in plain form, it just means chicken. The accusative form of tavuk is "tavuk + u=tavuğu" So, Sen tavuk yersin. You eat chicken. Sen tavuğu yersin. You eat THE chicken.
Thank you so much. I have tried to find out on several sites and never even got a clear differentiation for "piliç" and "tavuk". So "tavuk" is the chicken, eaten or alive, horoz the cock, "piliç" the young chicken. For completeness' sake - when is knowledge ever complete, though: what is the hen called?