A kinematically complete measurement was made of the Coulomb dissociation of ^ { 8 } B 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 ^ { 7 } Be ( p , \gamma ) ^ { 8 } B reaction . A first-order perturbation theory analysis of the reaction dynamics including E 1 , E 2 , and M 1 transitions was employed to extract the E 1 strength relevant to neutrino-producing reactions in the solar interior . By fitting the measured cross section from E _ { rel } = 130 keV to 400 keV , we find S _ { 17 } ( 0 ) = 17.8 ^ { +1.4 } _ { -1.2 } eV b .