  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.
