Abstract:  
The formation of relativistic jets by an accreting compact object is one of the fundamental mysteries of astrophysics.  While the theory is poorly understood, observations of relativistic jets from systems known as microquasars have led to a well-established phenomenology. Relativistic jets are not expected from sources with soft or supersoft X-ray spectra, although two such systems are known to produce relatively low-velocity bipolar outflows. Here we report optical spectra of an ultraluminous supersoft X-ray source  (ULS) in the nearby galaxy M81 (M81 ULS-1) showing blueshifted broad Hαemission lines, characteristic of baryonic jets with relativistic speeds. The time variable jets have projected velocities ~17 per cent of the speed of light, and seem similar to those in the prototype microquasar SS 433. Such relativistic jets are not expected to be launched from white dwarfs, but an origin from a black hole or neutron star in M81 ULS-1 is hard to reconcile with its constant soft X-rays. The completely unexpected presence of relativistic jets in a ULS challenges the canonical theories for jet formation, but can be explained by a long speculated super-critically accreting black hole with optically thick outflows.