We compute the stress tensor in the upper crust of southern California as a function of time and compare observed seismicity with the estimated stress at the time of each earthquake. Several recent developments make it possible to do this much more realistically than before: (1) a wealth of new geodetic and geologic data for southern California and (2) a catalog of moment tensors for all earthquakes with magnitudes larger than 6 since 1850 and larger than 5 since 1910. We model crustal deformation using both updated geodetic data and geologically determined fault slip rates. We subdivide the crust into elastic blocks, delineated by faults which move freely at a constant rate below a locking depth with a rate determined by the relative block motion. We compute normal and shear stresses on nodal planes for each earthquake in the catalog. We consider stress increments from previous earthquakes (seismic stress) and aseismic tectonic stress, both separately and in combination. The locations and mechanisms of earthquakes are best correlated with the aseismic shear stress. Including the cumulative coseismic effects from past earthquakes does not significantly improve the correlation. Correlations between normal stress and earthquakes are always very sensitive to the start date of the catalog, whether we exclude earthquakes very close to others and whether we evaluate stress at the hypocenter or throughout the rupture surface of an earthquake. Although the correlation of tectonic stress with earthquake triggering is robust, other results are unstable apparently because the catalog has so few earthquakes.