We report the first measurement of the parity-violating asymmetry in elastic electron scattering from the proton. The asymmetry depends on the neutral weak magnetic form factor of the proton which contains new information on the contribution of strange quark-antiquark pairs to the magnetic moment of the proton. We obtain the value GMZ = 0.34±0.09±0.04±0.05n.m. at Q2 = 0.1 (GeV/c)2.