Iron-based superconductors (FeSCs) are a fascinating family of materials in which several electronic bands and strong antiferromagnetic (AFM) correlations are key ingredients for competing ground states1–6, including antiferromagnetism, electronic nematicity and unconventional superconductivity. FeTe, unlike its superconducting isostructural counterpart FeSe, has long been considered an AFM metal sans superconductivity7–9. Here we use molecular-beam epitaxy (MBE) to grow FeTe films and perform post-growth annealing under a Te flux. By performing spin-polarized scanning tunnelling microscopy and spectroscopy (STM/S), we demonstrate that the AFM order in as-grown FeTe films is induced by interstitial Fe atoms that disrupt the ideal 1:1 stoichiometry. Notably, the removal of these interstitial Fe atoms through Te annealing yields stoichiometric FeTe films that show no AFM order and instead exhibit robust superconductivity with a critical temperature of about 13.5 K. This superconducting state is further confirmed by the observation of Cooper-pair tunnelling, zero electrical resistance and the Meissner effect. Therefore, our results demonstrate that stoichiometric FeTe is inherently a superconductor, overturning a long-held view that it is an AFM metal. This work clarifies the origin of superconductivity in FeTe-based heterostructures10–15 and demonstrates the importance of stoichiometry control in understanding the competition between antiferromagnetism and superconductivity in FeSCs.