The weak charge of the proton determines its coupling to the $Z^0$ boson. The distribution of weak charge is found to be dramatically different from the distribution of electric charge. The proton's weak radius $R_W$ = 1.545 $\pm$ 0.017 fm is 80% larger than its charge radius $R_{ch}$ $\approx$ 0.84 fm because of a very large pion cloud contribution. This large weak radius can be measured with parity violating electron scattering and may provide insight into the structure of the proton, various radiative corrections, and possible strange quark contributions.