We measured the ^ { 7 } Be ( p , \gamma ) ^ { 8 } B cross section from \bar { E } _ { cm } = 186 to 1200 keV , with a statistical-plus-systematic precision per point of better than \pm 5 \% . All important systematic errors were measured including ^ { 8 } B backscattering losses . We obtain S _ { 17 } ( 0 ) = 22.3 \pm 0.7 ( expt ) \pm 0.5 ( theor ) eV-b from our data at \bar { E } _ { cm } \leq 300 keV and the theory of Descouvemont and Baye .