We report measurements of the Sunyaev-Zel'dovich (SZ) effect in three high-redshift (0.89 < z < 1.03), X-ray selected galaxy clusters. The observations were obtained at 30 GHz during the commissioning period of a new, eight-element interferometer -- the Sunyaev-Zel'dovich Array (SZA) -- built for dedicated SZ effect observations. The SZA observations are sensitive to angular scales larger than those subtended by the virial radii of the clusters. Assuming isothermality and hydrostatic

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... for the intracluster medium, and gas-mass fractions consistent with those for clusters at moderate redshift, we calculate electron temperatures, gas masses, and total cluster masses from the SZ data. The SZ-derived masses, integrated approximately to the virial radii, are 1.9 ^+0.5_-0.4x10^14 solar masses for CLl1415.1+3612, 3.4^+0.6_-0.5x10^14 solar masses for CL1429.0+4241, and 7.2^+1.3_-0.9x10^14 solar masses for CL1226.9+3332. The SZ-derived quantities are in good agreement with the cluster properties derived from X-ray measurements.