We demonstrate optically tunable delays in a silicon-on-insulator planar waveguide based on slow light induced by stimulated Raman scattering (SRS). Inside an 8-mm-long nanoscale waveguide, we produce a group-index change of 0.15 and generate controllable delays as large as 4 ps for signal pulses as short as 3 ps. The scheme can be implemented at bandwidths exceeding 100 GHz for wavelengths spanning the entire low-loss fiber-optics communications window and thus represents an important step in the development of chip-scale photonics devices that process light with light.