  We use dispersion relations to evaluate the gamma-Z box contribution to
parity-violating electron scattering in the forward limit arising from the
axial-vector coupling at the electron vertex. The calculation makes full use of
the critical constraints from recent JLab data on electroproduction in the
resonance region as well as high energy data from HERA. At the kinematics of
the Qweak experiment, this gives a correction of 0.0047{+0.0011}{-0.0004}$ to
the Standard Model value 0.0713(8) of the proton weak charge. While the
magnitude of the correction is highly significant, the uncertainty is within
the anticipated experimental uncertainty of +- 0.003.
