  We introduce a notion of completely bounded holomorphic functions defined on
the open unit ball of an operator space. We endow the set of these functions
with an operator space structure, and in the scalar-valued case we identify an
operator space predual for it which is a noncommutative version of Mujica's
predual for the space of bounded holomorphic functions and satisfies similar
properties. In particular, our predual is a free holomorphic operator space in
the sense that it satisfies a linearization property for vector-valued
completely bounded holomorphic functions. Additionally, several different
operator space approximation properties transfer between the predual and the
domain.
