  Supersymmetric N=1, D=4 string vacua are known to be finite in perturbation
theory. However, the effective low energy D=4, N=1 field theory lagrangian does
not yield in general finite theories. In this note we present the first (to our
knowledge) such an example. It may be constructed in three dual ways: i) as a
$Z_3$, SO(32) heterotic orbifold; ii) as a Type -IIB, $Z_3$ orientifold with
only ninebranes and a Wilson line or iii) as a Type-IIB, $Z_6$ orientifold with
only fivebranes. The gauge group is $SU(4)^3$ with three chiral generations.
Although chiral, a subsector of the model is continuosly connected to a model
with global N=4 supersymmetry. From the $Z_6$, Type IIB orientifold point of
view the above connection may be understood as a transition of four dynamical
fivebranes from a fixed point to the bulk. The N=1 model is thus also expected
to be S-dual. We also remark that, using the untwisted dilaton and moduli
fields of these constructions as spurion fields, yields soft SUSY-breaking
terms which preserve finiteness even for N=0.
