We report the discovery of an eclipsing X-ray binary with a 3.62-hr period within 24″ of the center of the dwarf starburst galaxy NGC 4214 . The orbital period places interesting constraints on the nature of the binary , and allows for a few very different interpretations . The most likely possibility is that the source lies within NGC 4214 and has an X-ray luminosity , L _ { x } , of up to 7 \times 10 ^ { 38 } ergs s ^ { -1 } . In this case the binary may well be comprised of a naked He-burning donor star with a neutron-star accretor , though a stellar-mass black-hole accretor can not be completely excluded . There is no obvious evidence for a strong stellar wind in the X-ray orbital light curve that would be expected from a massive He star ; thus , the mass of the He star should be \lesssim 3 - 4 M _ { \odot } . If correct , this would represent a new class of very luminous X-ray binary – perhaps related to Cyg X-3 . Other less likely possibilities include a conventional low-mass X-ray binary that somehow manages to produce such a high X-ray luminosity and is apparently persistent over an interval of years ; or a foreground AM Her binary of much lower luminosity that fortuitously lies in the direction of NGC 4214 . Any model for this system must accommodate the lack of an optical counterpart down to a limiting magnitude of 22.6 in the visible .