  We initiate a systematic study of \emph{generic stability independence} and
introduce the class of \emph{treeless theories} in which this notion of
independence is particularly well-behaved. We show that the class of treeless
theories contains both binary theories and stable theories and give several
applications of the theory of independence for treeless theories. As a
corollary, we show that every binary NSOP$_{3}$ theory is simple.
