A kinematically complete measurement was made of the Coulomb dissociation of 8B nuclei on a Pb target at 83 MeV/nucleon. The cross section was measured at low relative energies in order to infer the astrophysical S factor for the 7Be(p,gamma)8B reaction. A first-order perturbation theory analysis including E1, E2, and M1 transitions was employed to extract the E1 strength relevant to neutrino-producing reactions in the solar interior. By fitting the measured cross section from E(rel) = 130 to 400 keV, we find S17(0) = 17.8(+1.4)(-1.2) eV b.