  We study quark and lepton mass matrix textures in a model containing an
additional $U(1)_X$ gauge symmetry with origins in string compactification. The
$U(1)_X$ symmetry is broken near the string scale, and we assume that the
anomalies are canceled by the Green-Schwarz mechanism. We also assume that
fermion mass matrices are generated by an additional scalar field through an
approach analogous to that of Froggatt and Nielsen. By requiring that
supersymmetry not be broken at the high scale, we can derive the vacuum
expectation value of this scalar field to then predict fermion masses and
mixings for any given $X$ charge assignment. We examine the possible solutions,
and although in the simplest model they do not completely agree with
experiment, the results are close enough to merit further inspection.
