  Additional Abelian gauge interactions are generic to string
compactifications. In heterotic string models, gauge coupling unification of
such forces and other gauge interactions is natural due to their common origin.
In this letter we study systematically the 1-loop running of the coupling
constants in effective vacua emerging from Z8 heterotic orbifold
compactifications that provide the matter spectrum of the MSSM plus some
vectorlike exotics, restricting to vacua that yield a non-anomalous U(1)'
symmetry, gauge coupling unification and the observed values of known gauge
couplings. We determine the low-energy value of the U(1)' coupling constant for
different scales of supersymmetry breakdown. We find that the U(1)' coupling
constant is quite restricted in string models to lie in the range 0.46-0.7 for
low-scale supersymmetry or 0.44-0.6 in other cases. We argue that the
phenomenology of these string vacua should be further explored to solve some
extant issues, such as the stability of the Higgs vacuum.
