Let be a bounded strongly convex domain in the complex space of dimension . For a fixed point , we consider the solution of a homogeneous complex Monge-Ampère equation with a simple pole at . We prove that such a solution enjoys many properties of the classical Poisson kernel in the unit disc and thus deserves to be called the pluricomplex Poisson kernel of with pole at . In particular we discuss extremality properties (such as a generalization of the classical Phragmen-Lindelof theorem), relations with the pluricomplex Green function of , uniqueness in terms of the associated foliation and boundary behaviors. Finally, using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions.