We use gravitational microlensing of the four images of the z = 0.658 quasar RXJ 1131-1231 to measure the sizes of the optical and X-ray emission regions of the quasar. The (face-on) scale length of the optical disk at rest frame 400 nm is R{sub l}ambda{sub ,O} = 1.3 x 10{sup 15} cm, while the half-light radius of the rest frame 0.3-17 keV X-ray emission is R{sub 1/2,X} = 2.3 x 10{sup 14} cm. The formal uncertainties are factors of 1.6 and 2.0, respectively. With the exception of the lower limit on the X-ray size, the results are very stable against any changes in the priors used in the analysis. Based on the Hbeta line width, we estimate that the black hole mass is M{sub 1131} approx = 10{sup 8} M{sub sun}, which corresponds to a gravitational radius of r{sub g} approx = 2 x 10{sup 13} cm. Thus, the X-ray emission is emerging on scales of approx10r{sub g} and the 400 nm emission on scales of approx70r{sub g} . A standard thin disk of this size should be significantly brighter than observed. Possible solutions are to have a flatter temperature profile or to scatter a large fraction of the optical flux on larger scales after it is emitted. While our calculations were not optimized to constrain the dark matter fraction in the lens galaxy, dark matter-dominated models are favored. With well-sampled optical and X-ray light curves over a broad range of frequencies, there will be no difficulty in extending our analysis to completely map the structure of the accretion disk as a function of wavelength.