We report an observational estimate of the rate of stellar tidal disruption flares (TDFs) in inactive galaxies, based on a successful search for these events among transients in galaxies using archival SDSS multi-epoch imaging data (Stripe 82). This search yielded 186 nuclear flares in galaxies, of which two are excellent TDF candidates. Because of the systematic nature of the search, the very large number of galaxies, the long time of observation, and the fact that non-TDFs were excluded without resorting to assumptions about TDF characteristics, this study provides an unparalleled opportunity to measure the TDF rate. To compute the rate of optical stellar tidal disruption events, we simulate our entire pipeline to obtain the efficiency of detection. The rate depends on the light curves of TDFs, which are presently still poorly constrained. Using only the observed part of the SDSS light curves gives a model-independent upper limit to the optical TDF rate: < 2 10^-4 per year per galaxy (90% CL). We develop three empirical models of the light curves, based on the two SDSS light curves and two more recent and better-sampled Pan-STARRS TDF light curves, leading to our best-estimate of the rate: (1.5 - 2.0)_{-1.3}^{+2.7} 10^-5 per year per galaxy. We explore the modeling uncertainties by considering two theoretically motivated light curve models, as well as two different relationships between black hole mass and galaxy luminosity, and two different treatments of the cutoff in the visibility of TDFs at large black hole mass. From this we conclude that these sources of uncertainty are not significantly larger than the statistical ones. Our results are applicable for galaxies hosting black holes with mass in the range of few million to 10^8 solar masses, and translates to a volumetric TDF rate of (4 - 8) 10^-8 per year per cubic Mpc.
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