The use of particle accelerators as photon sources has enabled advances in science and technology1. Currently the workhorses of such sources are storage-ring-based synchrotron radiation facilities2-4 and linear-accelerator-based free-electron lasers5-14. Synchrotron radiation facilities deliver photons with high repetition rates but relatively low power, owing to their temporally incoherent nature. Free-electron lasers produce radiation with high peak brightness, but their repetition rate is limited by the driving sources. The steady-state microbunching15-22 (SSMB) mechanism has been proposed to generate high-repetition, high-power radiation at wavelengths ranging from the terahertz scale to the extreme ultraviolet. This is accomplished by using microbunching-enabled multiparticle coherent enhancement of the radiation in an electron storage ring on a steady-state turn-by-turn basis. A crucial step in unveiling the potential of SSMB as a future photon source is the demonstration of its mechanism in a real machine. Here we report an experimental demonstration of the SSMB mechanism. We show that electron bunches stored in a quasi-isochronous ring can yield sub-micrometre microbunching and coherent radiation, one complete revolution after energy modulation induced by a 1,064-nanometre-wavelength laser. Our results verify that the optical phases of electrons can be correlated turn by turn at a precision of sub-laser wavelengths. On the basis of this phase correlation, we expect that SSMB will be realized by applying a phase-locked laser that interacts with the electrons turn by turn. This demonstration represents a milestone towards the implementation of an SSMB-based high-repetition, high-power photon source.