In order to investigate the dependence of quasar optical-UV variability on fundamental physical parameters like black hole mass, we have matched quasars from the QUEST1 variability survey with broad-lined objects from the SDSS. Black hole masses and bolometric luminosities are estimated from Sloan spectra, and variability amplitudes from the QUEST1 light curves. Long-term variability amplitudes (rest-frame time scales 0.5--2 yrs) are found to correlate with black hole mass at the 99% significance level or better. This means that quasars with larger black hole masses have larger percentage flux variations. Partial rank correlation analysis shows that the correlation cannot explained by obvious selection effects inherent to flux-limited samples. We discuss whether the correlation is a manifestation of a relation between BH mass and accretion disk thermal time scales, or if it is due to changes in the optical depth of the accretion disk with black hole mass. Perhaps the most likely explanation is that the more massive black holes are starving, and produce larger flux variations because they do not have a steady inflow of gaseous fuel.