Earthquake predictability depends, in part, on the degree to which sudden slip is preceded by slow aseismic slip. Recently, observations of deep tremor have enabled inferences of deep slow slip even when detection by other means is not possible, but these data are limited to certain areas and mostly the last decade. The region near Parkfield, California, provides a unique convergence of several years of high-quality tremor data bracketing a moderate earthquake, the 2004 magnitude 6.0 event. Here, I present detailed observations of tectonic tremor from mid-2001 through 2008 that indicate deep fault slip both before and after the Parkfield earthquake that cannot be detected with surface geodetic instruments. While there is no obvious short-term precursor, I find unidirectional tremor migration accompanied by elevated tremor rates in the 3 months prior to the earthquake, which suggests accelerated creep on the fault ∼16 km beneath the eventual earthquake hypocenter.