Terrestrial gamma-ray flashes (TGFs) are transient gamma-ray emissions from thunderstorms, generated by electrons accelerated to relativistic energies in electric fields. Elves are ultraviolet and optical emissions excited in the lower ionosphere by electromagnetic waves radiated from lightning current pulses. We observed a TGF and an associated elve using the Atmosphere-Space Interactions Monitor on the International Space Station. The TGF occurred at the onset of a lightning current pulse that generated an elve, in the early stage of a lightning flash. Our measurements suggest that the current onset is fast and has a high amplitude-a prerequisite for elves-and that the TGF is generated in the electric fields associated with the lightning leader.