We report a measurement of the neutrino-electron elastic scattering rate from {sup 8}B solar neutrinos based on a 123 kton-day exposure of KamLAND. The background-subtracted electron recoil rate, above a 5.5-MeV analysis threshold is 1.49 {+-} 0.14(stat) {+-} 0.17(syst) events per kton-day. Interpreted as due to a pure electron flavor flux with a {sup 8}B neutrino spectrum, this corresponds to a spectrum integrated flux of 2.77 {+-} 0.26(stat) {+-} 0.32(syst) x 10{sup 6} cm{sup -2}s{sup -1}. The analysis threshold is driven by {sup 208}Tl present in the liquid scintillator, and the main source of systematic uncertainty is due to background from cosmogenic {sup 11}Be. The measured rate is consistent with existing measurements and with standard solar model predictions which include matter-enhanced neutrino oscillation.