We have measured the parity-violating electroweak asymmetry in the elastic scattering of polarized electrons from the proton. The result is A = -14.60 +- 0.94(stat) +- 0.54(syst) ppm at the kinematic point theta_lab = 12.3 degrees and Q^2 = 0.477 (GeV/c)^2. The measurement implies that the value for the strange form factor (G_E^s + 0.392 G_M^s)/(G_M^p/\mu_p) = 0.091 +- 0.054 +- 0.039, where the first error is experimental and the second arises from the uncertainties in electromagnetic form factors. This measurement is the first fixed-target parity violation experiment that used either a `strained' GaAs photocathode to produce highly polarized electrons or a Compton polarimeter to continuously monitor the electron beam polarization.