  We have identified 2XMM J125556.57+565846.4, at a distance of 600 pc, as a
binary system consisting of a normal star and a probable dormant neutron star.
Optical spectra exhibit a slightly evolved F-type single star, displaying
periodic Doppler shifts with a 2.76-day Keplerian circular orbit, with no
indication of light from a secondary component. Optical and UV photometry
reveal ellipsoidal variations with half the orbital period, due to the tidal
deformation of the F star. The mass of the unseen companion is constrained to
the range $1.1$--$2.1\,M_{\odot}$ at $3\sigma$ confidence, with the median of
the mass distribution at $1.4\,M_{\odot}$, the typical mass of known neutron
stars. A main-sequence star cannot masquerade as the dark companion. The
distribution of possible companion masses still allows for the possibility of a
very massive white dwarf. The companion itself could also be a close pair
consisting of a white dwarf and an M star, or two white dwarfs, although the
binary evolution that would lead to such a close triple system is unlikely.
Similar ambiguities regarding the certain identification of a dormant neutron
star are bound to affect most future discoveries of this type of
non-interacting system. If the system indeed contains a dormant neutron star,
it will become, in the future, a bright X-ray source and afterwards might even
host a millisecond pulsar.
