Evidence for the early development of convective instability in the thermal boundary layer associated with cooling plates has been found from gravity anomalies and residual sea surface heights derived from Seasat altimeter data. Subtle lineated patterns trending in the direction of plate motion in the hot spot reference frame are observed over the younger portions of the fast-moving Pacific and Indo-Australian plates. In particular, for the east central Pacific Ocean, the Seasat-derived data sets reveal lineations with (1) wavelengths in the range 150-500 km (perhaps increasing with plate age), and (2) peak-to-trough amplitudes of 5--20 mGal for gravity anomalies. The lineated pattern over the Pacific plate, which first becomes discernable over seafloor 5- to 10-m.y.-old west of the East Pacific Rise, is clearly oblique to the trends of the prominent Pacific-Farallon fracture zones. Onset of convective instability at such early ages can be understood if young oceanic lithosphere is underlain by a layer having a viscosity of about 1018 Pa s (1019 P), which is about 3 orders of magnitude less than mantle viscosity inferred from postglacial rebound studies. Recent numerical studies of convection in fluids with a temperature- and pressure-dependent viscosity support an early onset time for convective instability and low-viscosity zones in the upper mantle beneath young lithosphere. Such low-viscosity zones may correspond to similarly located regions of low shear wave velocities resolved through studies of surface waves.