The recently discovered correlation between black hole mass and stellar velocity dispersion provides a new method to determine the masses of black holes in active galaxies. We have obtained optical spectra of Markarian 501, a nearby gamma-ray blazar with emission extending to TeV energies. The stellar velocity dispersion of the host galaxy, measured from the calcium triplet lines in a 2"x3.7" aperture, is 372 +/- 18 km/s. If Mrk 501 follows the M-sigma correlation defined for local galaxies, then its central black hole has a mass of (0.9-3.4)x10^9 solar masses. This is significantly larger than some previous estimates for the central mass in Mrk 501 that have been based on models for its nonthermal emission. The host galaxy luminosity implies a black hole of 6x10^8 solar masses, but this is not in severe conflict with the mass derived from the M-sigma relation because the M_BH-L_bulge correlation has a large intrinsic scatter. Using the emission-line luminosity to estimate the bolometric luminosity of the central engine, we find that Mrk 501 radiates at an extremely sub-Eddington level of L/L_Edd ~ 10^-4. Further applications of the M-sigma relation to radio-loud active galactic nuclei may be useful for interpreting unified models and understanding the relationship between radio galaxies and BL Lac objects. Comment: To appear in ApJ Letters. 5 pages, 2 figures