We report the detection of weak gravitational lensing of faint, distant background galaxies by the rich, X-ray luminous cluster of galaxies MS 1054-03 at z = 0.83. This is the fist measurement of weak lensing by a bona fide cluster at such a high redshift. We detect tangential shear at the 5%-10% level over a range of radii 50 '' less than or similar to r less than or similar to 250 '' centered on the optical position of the cluster. Two-dimensional mass reconstruction using galaxies with 21.5 < I < 25.5 shows a strong peak which coincides with the peak of the smoothed cluster light distribution. Splitting this sample by magnitude (at I = 23.5) and color (at R-I = 0.7), we find that the brighter and redder subsamples are only very weakly distorted, indicating that the faint blue galaxies (FBGs), which dominate the shear signal, are relatively more distant. The derived cluster mass is quite sensitive to the N(z) for the FBGs. At one extreme, if all the FBGs are at z(s) = 3, then the mass within a 0.5 h(-1) Mpc aperture is (5.9 +/- 1.24) x 10(14) h(-1) M., and the mass-to-light ratio is M/L(V) = 350 +/- 70 h in solar units. For z(s) = 1.5 the derived mass is similar to 70% higher and M/L similar or equal to 580 h. If N(z) follows the no evolution model (in shape) then M/L similar or equal to 800 h, and if all the FBGs lie at z(s) less than or similar to 1 the required M/L exceeds 1600 h. These data provide clear evidence that large, dense mass concentrations existed at early epochs; that they can be weighed efficiently by weak lensing observations; and that, for a plausible cluster mass, most of the FBGs must lie at high redshift (z > 1).