Following earthquakes, faults are often observed to continue slipping aseismically. It has been proposed that this afterslip occurs on parts of the fault with rate-strengthening friction that are stressed by the main shock, but our understanding has been limited by a lack of immediate, high-resolution observations. Here we show that the behavior of afterslip following the 2014 South Napa earthquake in California varied over distances of only a few kilometers. This variability cannot be explained by coseismic stress changes alone. We present daily positions from continuous and survey GPS sites that we remeasured within 12 h of the main shock and surface displacements from the new Sentinel-1 radar mission. This unique geodetic data set constrains the distribution and evolution of coseismic and postseismic fault slip with exceptional resolution in space and time. We suggest that the observed heterogeneity in behavior is caused by lithological controls on the frictional properties of the fault plane.