Adding optical functionality to a silicon microelectronic chip is one of the most challenging problems of materials research. Silicon is an indirect-bandgap semiconductor and so is an inefficient emitter of light. For this reason, integration of optically functional elements with silicon microelectronic circuitry has largely been achieved through the use of direct-bandgap compound semiconductors. For optoelectronic applications, the key device is the light source--a laser. Compound semiconductor lasers exploit low-dimensional electronic systems, such as quantum wells and quantum dots, as the active optical amplifying medium. Here we demonstrate that light amplification is possible using silicon itself, in the form of quantum dots dispersed in a silicon dioxide matrix. Net optical gain is seen in both waveguide and transmission configurations, with the material gain being of the same order as that of direct-bandgap quantum dots. We explain the observations using a model based on population inversion of radiative states associated with the Si/SiO2 interface. These findings open a route to the fabrication of a silicon laser.