Stellar-mass black holes are the final remnants of stars born with more than 15 solar masses. Billions are expected to reside in the Local Group, yet only a few are known, mostly detected through X-rays emitted as they accrete material from a companion star. Here, we report on VFTS 243: a massive X-ray-faint binary in the Large Magellanic Cloud. With an orbital period of 10.4 d, it comprises an O-type star of 25 solar masses and an unseen companion of at least nine solar masses. Our spectral analysis excludes a non-degenerate companion at a 5σ confidence level. The minimum companion mass implies that it is a black hole. No other X-ray-quiet black hole is unambiguously known outside our Galaxy. The (near-)circular orbit and kinematics of VFTS 243 imply that the collapse of the progenitor into a black hole was associated with little or no ejected material or black-hole kick. Identifying such unique binaries substantially impacts the predicted rates of gravitational-wave detections and properties of core-collapse supernovae across the cosmos.