Pore fluid pressure is a key parameter governing both the shear strength of faults and the conditions for seismic and tsunamigenic slip on subduction zone megathrusts. However, quantitative constraints on this parameter based on in situ data in these, or any, faults have proven elusive. Using seismic interval velocities derived from a three-dimensional seismic reflection survey, we compute porosity, fluid pressure, and effective stress at the plate interface in the Nankai Trough subduction zone (offshore southwestern Japan) to 20 km down the fault dip using well-constrained, locally calibrated empirical relationships between velocity, porosity, and effective stress. We show that the fault and immediately subjacent footwall are nearly undrained, implying that the subduction megathrust slips under a shear stress of <~4 MPa throughout the study area and that fault shear strength remains nearly constant despite increasing depth. Computed pore pressures are in excellent agreement with independent hydrological model results, and are perhaps the best constrained and most spatially extensive estimates of pore pressure within a plate boundary fault system and subducted sediments. This elevated pore pressure offers a plausible and quantifiable explanation for the mechanical weakness of the fault and the suppression of stick-slip seismogenic behavior in the updip region.