We propose a precision measurement of the parity nonconserving left-right asymmetry in the scattering of longitudinally polarized electrons from the atomic electrons in a hydrogen target (MMller scattering) in End Station A. The asymmetry measures the eeective pseudo-scalar weak neutral current coupling governing MMller scattering (g ee g Ve g Ae) at an average Q 2 of 0.03 (GeV/c) 2 and is proportional to (1 4 ? sin 2 W), where sin 2 W is the electroweak mixing angle. We plan to measure the asymmetry to a precision of 7 10 ?9 , which would measure g ee to a relative precision of 6%, corresponding to (sin 2 W) 0:0007. The dominant systematic error is expected to come from the measurement of the beam polarization, corresponding to (sin 2 W) syst 0:0003. The ability to measure a purely leptonic weak neutral current coupling with such precision at low Q 2 is unprecedented. A comparison of such a measurement with precision asymmetry measurements at the Z 0 resonance would provide the rst statistically signiicant measurement of sin 2 ^ W (M 2 Z)?sin 2 ^ W (0), testing the electroweak theory at the quantum loop level, for the rst time away from the Z 0 resonance. The measurement has unique sensitivity to new electron-electron interactions at the TeV scale, accessing the electron compositeness scale at the same level as the ultimate reach of LEP-200.