We theoretically demonstrate that a system formed by two coupled graphene sheets enables a negative damping regime wherein graphene plasmons are pumped by a direct current. This effect is triggered by electrons drifting through one of the graphene sheets and leads to wave instabilities and a spontaneous light emission (spasing) in the midinfrared range. It is shown that there is a deep link between the drift-induced instabilities and wave instabilities in moving media, as both result from the hybridization of oscillators with oppositely signed frequencies. With a thickness of a few nanometers and wide spectral tunability, the proposed structure may find interesting applications in nanophotonic circuitry as an on-chip light source.