We have monitored spectroscopically the classical T Tauri star UZ Tau East. Most observations were obtained with the Intermediate Dispersion Spectrograph at the Isaac Newton Telescope in La Palma Observatory. Several additional spectra were obtained with other telescopes at La Palma, ESO and Lick observatories. Radial velocities were measured via cross correlation with UZ Tau West. In total we have so far 18 radial velocity measurements spanning 2627 days (Nov 1988 -- March 1996). The radial-velocity data are well fit (sigma =2.3 km s(-1) ) with a single-line orbit solution having a period of 19.1 days, an eccentricity e=0.28, and a K of 17 km s(-1) . The projected primary semi-major axis is a sini = 0.03 AU. The orbit parameters are not yet definitive because the phase sampling is not thorough. After GW Ori and DQ Tau, UZ Tau E is the third classical T Tauri spectroscopic binary for which an orbit has been derived. A massive (0.06 Msun) circumbinary disk has been resolved at millimeter wavelengths (Jensen et al. 1996, ApJ, in press). Interestingly, UZ Tau E has a power-law infrared spectral energy distribution with no evident dip suggesting an inner region cleared by the binary. In addition, UZ Tau E is spectroscopically active with both veiling and emission lines, indicative of active accretion at a stellar surface despite the close companion. With this discovery UZ Tau becomes a quadruple system, as UZ Tau West is a speckle binary with a projected separation of 50 AU.