  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 of up to 7 e38
ergs/s. 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 cannot 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 <3-4 solar
masses. 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.
