The Qweak experiment at Jefferson Lab aims to make a 4\% measurement of the parity-violating asymmetry in elastic scattering at very low $Q^2$ of a longitudinally polarized electron beam on a proton target. The experiment will measure the weak charge of the proton, and thus the weak mixing angle at low energy scale, providing a precision test of the Standard Model. Since the value of the weak mixing angle is approximately 1/4, the weak charge of the proton $Q^p_w=1-4\sin^2\theta_w$ is suppressed in the Standard Model, making it especially sensitive to the value of the mixing angle and also to possible new physics. The experiment is approved to run at JLab, and the construction plan calls for the hardware to be ready to install in Hall C in 2007. The experiment will be a 2200 hour measurement, employing: an 80\% polarized, 180 $\mu$ A, 1.2 GeV electron beam; a 35 cm liquid hydrogen target; and a toroidal magnet to focus electrons scattered at 9$\deg$, a small forward angle corresponding to $Q^2 = 0.03~{\rm (GeV/c)^2}$. With these kinematics the systematic uncertainties from hadronic processes are strongly suppressed. To obtain the necessary statistics the experiment must run at an event rate of over 6 GHz. This requires current mode detection of the scattered electrons, which will be achieved with synthetic quartz \v{C}erenkov detectors. A tracking system will be used in a low-rate counting mode to determine average $Q^2$ and the dilution factor of background events.