  The X-ray source RX J0806+15 was discovered using ROSAT, and shows an X-ray
light curve with a prominent modulation on a period of 321.5 sec. We present
optical observations in which we report the detection of its optical
counterpart. We find an optical period consistent with the X-ray period. We do
not find convincing evidence for a second period in the data: this implies the
321.5 sec period is the orbital period. As such it would be the shortest period
stellar binary system yet known. We discuss the nature of this system. We
conclude that an isolated neutron star and an intermediate polar interpretation
is unlikely and that a double degenerate interpretation is the most likely.
