ABSTRACT 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-d Keplerian circular orbit, with no indication of light from a secondary component. Optical and UV photometry reveal ellipsoidal modulation 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 of 1.1–$2.1\, \mathrm{M}_{⊙ }$ at 3σ confidence, with the median of the mass distribution at $1.4\, \mathrm{M}_{⊙ }$, 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.