CP-violating phases which contribute to the electric dipole moment (ED
M) of the neutron are considered in the context of orbifold compactifi
cation of the heterotic string. In particular, we study the situation
where CP is spontaneously broken by moduli fields acquiring, in genera
l, complex expectation values at the minimum of duality invariant low
energy effective potentials. We show, by explicit minimization of such
a potential in the case of the Z(6) - IIb orbifold, that it is the pr
esence of so called Green-Schwarz anomaly coefficients delta(GS)(i), t
hat leads to significant CP violating expectation values of the moduli
. By evaluating the soft supersymmetry breaking moduli dependent A and
B terms in this model, we find that the experimental bounds phi(A), p
hi(B) less than or equal to 5 x 10(-3) are exceeded for a particular r
ange of values of the auxiliary field of the S modulus.