A D-finite power series satisfies a system of linear partial differential equations with polynomial coefficients of special type. This class of power series has been systematically investigated by Stanley in his book Enumerative Combinatorics (Volume II). We prove that a multivariate D-finite power series with coefficients from a finite set is rational. This generalizes a rationality theorem of van der Poorten and Shparlinski in 1996. As an application, we will show how this result can be used to study the nonnegative integer points on algebraic varieties. This is a joint work with Jason P. Bell.