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Microquasars are laboratories for the study of jets of relativistic particles produced by accretion onto a spinning black hole. Microquasars are near enough to allow detailed imaging of spatial features across the multiwavelength spectrum. The recent extension measurement of the spatial morphology of a microquasar, SS 433, to TeV gamma rays 1 localizes the acceleration of electrons at shocks in the jet far from the black hole 2 . V4641 Sagittarii (V4641 Sgr) is a similar binary system with a black hole and B-type main-sequence companion star and has an orbit period of 2.8 days (refs.  3,4 ). It stands out for its super-Eddington accretion 5 and for its radio jet, which is one of the fastest superluminal jets in the Milky Way. Previous observations of V4641 Sgr did not report gamma-ray emission 6 . Here we report TeV gamma-ray emission from V4641 Sgr that reveals particle acceleration at similar distances from the black hole as SS 433. Furthermore, the gamma-ray spectrum of V4641 Sgr is among the hardest TeV spectra observed from any known gamma-ray source and is detected above 200 TeV. Gamma rays are produced by particles, either electrons or protons, of higher energies. Because energetic electrons lose energy more quickly the higher their energy, such a spectrum either very strongly constrains the electron-production mechanism or points to the acceleration of high-energy protons. This suggests that large-scale jets from microquasars could be more common than previously expected and that they could be a notable source of galactic cosmic rays 7-9 ., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)