The astrophysical factor for the proton weak capture on 3He is calculated with correlated hyperspherical harmonic wave functions corresponding to a realistic Hamiltonian consisting of the Argonne v(18) two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak current has vector and axial-vector components with one- and many-body terms. All possible transitions connecting any of the p 3He S- and P-wave channels to 4He are considered. The S factor at a p 3He center-of-mass energy of 10 keV is predicted to be 10. 1x10(-20) keV b, a factor of approximately 4.5 larger than the value adopted in the standard solar model. The P-wave transitions are found to contribute about 40% of the calculated S factor.