Having a nucleus darker than charcoal, comets are usually detected from Earth through the emissions from their coma. The coma is an envelope of gas that forms through the sublimation of ices from the nucleus as the comet gets closer to the Sun. In the far-ultraviolet portion of the spectrum, observations of comae have revealed the presence of atomic hydrogen and oxygen emissions. When observed over large spatial scales as seen from Earth, such emissions are dominated by resonance fluorescence pumped by solar radiation. Here, we analyse atomic emissions acquired close to the cometary nucleus by the Rosetta spacecraft and reveal their auroral nature. To identify their origin, we undertake a quantitative multi-instrument analysis of these emissions by combining coincident neutral gas, electron and far-ultraviolet observations. We establish that the atomic emissions detected from Rosetta around comet 67P/Churyumov-Gerasimenko at large heliocentric distances result from the dissociative excitation of cometary molecules by accelerated solar-wind electrons (and not by electrons produced from photo-ionization of cometary molecules). Like the discrete aurorae at Earth and Mars, this cometary aurora is driven by the interaction of the solar wind with the local environment. We also highlight how the oxygen line O I at wavelength 1,356 Å could be used as a tracer of solar-wind electron variability.