We have obtained 17 moderate-resolution (~2.5 A) optical spectra of the Galactic X-ray Nova Velorum 1993 in quiescence with the Keck-II telescope. The orbital period (P) is 0.285206 +/- 0.0000014 d, and the semiamplitude (K_2) is 475.4 +/- 5.9 km/s. Our derived mass function, f(M_1) = PK_2^3 /2 pi G = 3.17 +/- 0.12 M_sun, is close to the conventional absolute limiting mass for a neutron star (~ 3.0-3.2 M_sun) -- but if the orbital inclination i is less than 80 degrees (given the absences of

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... pses), then M_1 is greater than 4.2-4.4 M_sun for nominal secondary-star masses of 0.5 M_sun (M0) to 0.65 M_sun (K6). The primary star is therefore almost certainly a black hole rather than a neutron star. The velocity curve of the primary from H-alpha emission has a semiamplitude (K_1) of 65.3 +/- 7.0 km/s, but with a phase offset by 237 degrees (rather than 180 degrees) from that of the secondary star. The nominal mass ratio q = M_2/M_1 = K_1/K_2 = 0.137 +/- 0.015, and hence for M_2 = 0.5-0.65 M_sun we derive M_1 = 3.64-4.74 M_sun. An adopted mass M_1 ~ 4.4 M_sun is significantly below the typical value of ~ 7 M_sun found for black holes in other low-mass X-ray binaries. Keck observations of MXB 1659-29 (V2134 Oph) in quiescence reveal a probable optical counterpart at R = 23.6 +/- 0.4 mag.