Optical spectra were obtained of the optical counterpart of the high-latitude (b~=62deg) soft X-ray transient XTE J1118+480 near its quiescent state (R~=18.3) with the new 6.5 m Multiple Mirror Telescope and the 4.2 m William Herschel Telescope. The spectrum exhibits broad, double-peaked emission lines of hydrogen (FWHM~=2400 km s-1) arising from an accretion disk superposed with absorption lines of a late-type secondary star. Cross-correlation of the 27 individual spectra with late-type stellar template spectra reveals a sinusoidal variation in radial velocity with amplitude K=701+/-10 km s-1 and orbital period P=0.169930+/-0.000004 days. The mass function, 6.1+/-0.3 Msolar, is a firm lower limit on the mass of the compact object and strongly implies that it is a black hole. We estimate the spectral type of the secondary to be K7 V-M0 V, and that it contributes 28%+/-2% of the light in the 5800-6400 Å region on 2000 November 20, increasing to 36%+/-2% by 2001 January 4 as the disk faded. Photometric observations (R-band) with the Instituto de Astrofísica de Canarias 0.8 m telescope reveal ellipsoidal light variations of full amplitude 0.2 mag. Modeling of the light curve gives a large mass ratio (M1/M2~20) and a high orbital inclination (i=81deg+/-2deg). Our combined fits yield a mass of the black hole in the range M1=6.0-7.7 Msolar (90% confidence) for plausible secondary star masses of M2=0.09-0.5 Msolar. The photometric period measured during the outburst is 0.5% longer than our orbital period and probably reflects superhump modulations, as observed in some other soft X-ray transients. The estimated distance is d=1.9+/-0.4 kpc, corresponding to a height of 1.7+/-0.4 kpc above the Galactic plane. The spectroscopic, photometric, and dynamical results indicate that XTE J1118+480 is the first firmly identified black hole X-ray system in the Galactic halo. Based in part on observations obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution.