  The astrophysical S-factor for proton-proton weak capture is calculated in
chiral effective field theory over the center-of-mass relative-energy range
0--100 keV. The chiral two-nucleon potential derived up to
next-to-next-to-next-to leading order is augmented by the full electromagnetic
interaction including, beyond Coulomb, two-photon and vacuum-polarization
corrections. The low-energy constants (LEC's) entering the weak current
operators are fixed so as to reproduce the A=3 binding energies and magnetic
moments, and the Gamow-Teller matrix element in tritium beta decay.
Contributions from S and P partial waves in the incoming two-proton channel are
retained. The S-factor at zero energy is found to be S(0)=(4.030 +/- 0.006) x
10^{-23} MeV fm^2, with a P-wave contribution of 0.020 x 10^{-23} MeV fm^2. The
theoretical uncertainty is due to the fitting procedure of the LEC's and to the
cutoff dependence.
