We investigate an ongoing silent thrust event in the Tokai seismic gap along the Suruga-Nankai Trough, central Japan. Prior to the event, continuous GPS data from April 1996 to the end of 1999 show that this region displaced ~2 cm/yr to the northwest relative to the landward plate. The GPS time series show an abrupt change in rate in mid-June 2000 that continues as of mid-2005. We model this transient deformation, which we refer to as the Tokai slow thrust slip event, as caused by slip on the interface between the Philippine Sea and Amurian plates. The spatial and temporal distribution of slip rate is estimated with Kalman filter based inversion methods. Our inversions reveal two slow subevents. The first initiated in late June 2000 slightly before the Miyake-jima eruption. The locus of slip then propagated southeast in the second half of 2000, with maximum slip rates of about 15 cm/yr through 2001. A second locus of slip initiated to the northeast in early 2001. The depth of the slip zone is about 25 km, which may correspond to the transition zone from a seismogenic to a freely sliding zone. The cumulative moment magnitude of the slow slip event up to November 2002 is Mw ~ 6.8. We calculate shear stress changes on the plate interface from the slip histories. Stress change as a function of slip rate shows trajectories similar to that inferred for high-speed ruptures; however, the maximum velocity is 8 orders of magnitude less than in normal earthquakes.