  We prove a theorem of Hadamard-Stoker type: a connected locally convex
complete hypersurface immersed in $H^n \times R$ (n>1), where $H^n$ is
n-dimensional hyperbolic space, is embedded and homeomorphic either to the
n-sphere or to $R^n$. In the latter case it is either a vertical graph over a
convex domain in $H^n$ or has what we call a simple end.
