Optical spectra were obtained of the optical counterpart of the high-latitu
de (b similar or equal to 62 degrees) soft X-ray transient XTE J1118+480 ne
ar its quiescent state (R similar or equal to 18.3) with the new 6.5 m Mult
iple Mirror Telescope and the 4.2 m William Herschel Telescope. The spectru
m exhibits broad, double-peaked emission lines of hydrogen (FWHM similar or
equal to 2400 km s(-1)) arising from an accretion disk superposed with abs
orption lines of a late-type secondary star. Cross-correlation of the 27 in
dividual spectra with late-type stellar template spectra reveals a sinusoid
al variation in radial velocity with amplitude K=701 +/- 10 km s(-1) and or
bital period P=0.169930 +/- 0.000004 days. The mass function, 6.1 +/- 0.3 M
-., is a firm lower limit on the mass of the compact object and strongly im
plies that it is a black hole. We estimate the spectral type of the seconda
ry to be K7 V-M0 V, and that it contributes 28% +/- 2% of the light in the
5800-6400 Angstrom region on 2000 November 20, increasing to 36% +/- 2% by
2001 January 4 as the disk faded. Photometric observations (R-band) with th
e Instituto de de Canarias 0.8 m telescope reveal ellipsoidal Astrofisica l
ight variations of full amplitude 0.2 mag. Modeling of the light curve give
s a large mass ratio (M-1/M-2 similar to 20) and a high orbital inclination
(i = 81 degrees +/- 2 degrees). Our combined fits yield a mass of the blac
k hole in the range M-1 = 6.0-7.7 M-. (90% confidence) for plausible second
ary star masses of M-2 = 0.09-0.5 M-.. The photometric period measured duri
ng the outburst is 0.5% longer than our orbital period and probably reflect
s superhump modulations, as observed in some other soft X-ray transients. T
he 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, a
nd dynamical results indicate that XTE J1118+480 is the first firmly identi
fied black hole X-ray system in the Galactic halo.