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 G Z M 0.34 6 0.09 6 0.04 6 0.05 n.m. at Q 2 0.1 ͑GeV͞c͒ 2 . [S0031-9007(97)03181-5] PACS numbers: 13.60. Fz, 11.30.Er, 13.40.Gp, 14.20.Dh The measurement of strange quark-antiquark (ss) effects in the nucleon offers a unique window to study the effects of the qq "sea" at low momentum transfers. This information is an important clue to the dynamical effects of QCD that are responsible for form factors in the nonperturbative regime, and may lead to new insight into the origins of these effects.It has been shown [1] that the neutral weak current can be used to determine the ss contributions to nucleon form factors. The magnetic moment is one important nucleon property that can be studied in this fashion. The neutral weak magnetic form factor of the proton can be measured in parity-violating electron scattering, [2], thus providing information on the ss content of the nucleon's magnetic moment. In this Letter, we report the first such measurement and obtain the first direct experimental data relevant to determination of the strange magnetic moment of the proton.To lowest order (tree-level), the neutral weak magnetic form factor of the proton G Z M can be related to nucleon electromagnetic form factors and a contribution from strange quarks: As mentioned above, the quantity G Z M for the proton can be measured via elastic parity-violating electron scattering at backward angles [2]. The difference in cross sections for right and left handed incident electrons arises from interference of the electromagnetic and neutral weak amplitudes, and so contains products of electromagnetic and neutral weak form factors. The expression for elastic scattering from the proton is given by