  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 H\alpha\
emission 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 may
possibly be explained by a long speculated super-critically accreting black
hole with optically thick outflows
