Spectroscopic observations of the fast X-ray transient and superluminal jet source SAX J1819.3-2525 (V4641 Sgr) reveal a best-fitting period of P-spect = 2.81678 +/- 0.00056 days and a semiamplitude of K-2 = 211.0 +/- 3.1 km s(-1). The optical mass function is f(M) = 2.74 +/- 0.12 M-. We find a photometric period of P-photo = 2.81730 +/- 0.0001 days using a light curve measured from photographic plates. The folded light curve resembles an ellipsoidal light curve with two maxima of roughly equal height and two minima of unequal depth per orbital cycle. The secondary star is a late B-type star that has evolved off the main sequence. Using a moderate resolution spectrum (R = 7000) we measure T-eff = 10500 +/- 200 K, log g = 3.5 +/- 0.1, and V-rot sin i = 123 +/- 4 km s(-1) (1 sigma errors). Assuming synchronous rotation, our measured value of the projected rotational velocity implies a mass ratio of Q equivalent to M-1/M-2 = 1.50 +/- 0.008 (1 sigma). The lack of X-ray eclipses implies an upper limit to the inclination of i less than or equal to 70 degrees .7. On the other hand, the large amplitude of the folded light curve (approximate to0.5 mag) implies a large inclination (i greater than or similar to 60 degrees). Using the above mass function, mass ratio, and inclination range, the mass of the compact object is in the range 8.73 less than or equal to M1 less than or equal to 11.7 M.and the mass of the secondary star is in the range 5.49 less than or equal to M-2 less than or equal to 8.14 M. (90% confidence). The mass of the compact object is well above the maximum mass of a stable neutron star, and we conclude that V4641 Sgr contains a black hole. The B-star secondary is by far the most massive, the hottest, and the most luminous secondary of the dynamically confirmed black hole X-ray transients. We find that the alpha -process elements nitrogen, oxygen, calcium, magnesium, and titanium may be over-abundant in the secondary star by factors of 2-10 times with respect to the Sun. Finally, assuming E(B-V) = 0.32 +/- 0.10, we find a distance 7.4 less than or equal to d less than or equal to 12.31 kpc (90% confidence). This large distance and the high proper motions observed for the radio counterpart make V4641 Sgr possibly the most superluminal galactic source known, with an apparent expansion velocity of greater than or similar to9.2c and a bulk Lorentz factor of Gamma greater than or similar to 9.5, assuming that the jets were ejected during one of the bright X-ray flares observed with the Rossi X-ray Timing Explorer.