A Big Picard Theorem for Holomorphic Maps into Complex Projective Space We prove a big Picard type extension theorem for holomorphic maps $f\from X-A \rightarrow M$, where $X$ is a complex manifold, $A$ is an analytic subvariety of $X$, and $M$ is the complement of the union of a set of hyperplanes in ${\Bbb P}^n$ but is not necessarily hyperbolically imbedded in ${\Bbb P}^n$. Category:32H30