Josephson flux-flow oscillators (FFOs) have been used as an on-chip local oscillator at frequencies up to 650 GHz. An autonomous FFO linewidth of about 1 MHz was measured in the resonant regime at V_b<950 µV for niobium-aluminium oxide-niobium tunnel junctions, while considerably larger values were reported at higher voltages. To overcome this fundamental linewidth broadening we propose an on-chip Cherenkov radiation flux-flow oscillator (CRFFO). It consists of a long Josephson junction and a superconducting slow-wave transmission line that modifies significantly the junction dispersion relation. Two superconductor-insulator-superconductor junction detectors are connected to both the long Josephson junction and the slow-wave line to determine the available microwave power. The power is measured at different CRFFO biasing conditions. Both a forward wave and a backward wave oscillation regime are observed. An FFO and a CRFFO with the same junction parameters are compared.