We have undertaken a new ground-based monitoring campaign to improve the estimates of the mass of the central black hole in NGC 4151. We measure the lag time of the broad H beta line response compared to the optical continuum at 5100 A and find a lag of 6.6 (+1.1/-0.8) days. We combine our data with the recent reanalysis of UV emission lines by Metzroth et al. to calculate a weighted mean of the black hole mass, M_BH = 4.57 (+0.57/-0.47) x 10^7 M_sun. The absolute calibration of the black hole mass is based on normalization of the AGN black hole mass - stellar velocity dispersion (M_BH - sigma_*) relationship to that of quiescent galaxies by Onken et al. The scatter in the M_BH - sigma_* relationship suggests that reverberation-mapping based mass measurements are typically uncertain by a factor of 3-4.