We report the first measurement of the parity-violating asymmetry in e
lastic electron scattering from the proton. The asymmetry depends on t
he neutral weak magnetic form factor of the proton which contains new
information on the contribution of strange quark-antiquark pairs to th
e magnetic moment of the proton. We obtain the value G(M)(Z) = 0.34 +/
- 0.09 +/- 0.04 +/- 0.05 n.m. at Q(2) = 0.1 (GeV/c)(2).