A pumping system for a transmission system having a single pump functionally connected to a mechanical power source and an electrical power source is provided. The connections between the pump and the mechanical power source and electrical power source include at least one roller clutch, which permits only one of the power sources to drive the pump at any given time. Additionally, the functional connections, which may be chains, provide that the pump and the electrical power source may be located non-coaxial with the center axis of the transmission system, as may be preferred for improved packaging. The dual-chain and roller clutch pumping system is appropriate for gasoline/electric hybrid vehicles where pumping may be necessary when the engine is off and limited packaging space is available in the transmission housing.