  We propose a new precision measurement of parity-violating electron
scattering on the proton at very low Q^2 and forward angles to challenge
predictions of the Standard Model and search for new physics. A unique
opportunity exists to carry out the first precision measurement of the proton's
weak charge, $Q_W =1 - 4\sin^2\theta_W$. A 2200 hour measurement of the parity
violating asymmetry in elastic ep scattering at Q^2=0.03 (GeV/c)^2 employing
180 $\mu$A of 85% polarized beam on a 35 cm liquid Hydrogen target will
determine the proton's weak charge with approximately 4% combined statistical
and systematic errors. The Standard Model makes a firm prediction of $Q_W$,
based on the running of the weak mixing angle from the Z0 pole down to low
energies, corresponding to a 10 sigma effect in this experiment.
