Coherent electron transport is studied in an electrically driven quantum cascade structure. Ultrafast quantum transport from the injector into the upper laser state is investigated by midinfrared pump-probe experiments directly monitoring the femtosecond saturation and subsequent recovery of electrically induced optical gain. We demonstrate for the first time pronounced gain oscillations giving evidence for a coherent electron motion. The coexistence of a long dephasing time of quantum coherence and high Coulomb scattering rates in the injector points to the occurrence of scattering-induced coherence in electron transport.