  In the error box of 3EG J1835+5918, the brightest as-yet unidentified EGRET
source at intermediate Galactic latitude, we find a weak, ultrasoft X-ray
source at energies E < 0.3 keV in the ROSAT All-Sky Survey. Deep optical
imaging at the location of this source, as pinpointed by an observation with
the ROSAT HRI, reveals a blank field to a limit of V > 25.2. The corresponding
lower limit on f_X/f_V is 300, which signifies that the X-ray source is
probably a thermally emitting neutron star. Considering our previous complete
multiwavelength survey of the 3EG J1835+5918 region which failed to find any
other notable candidate for identification with 3EG J1835+5918, we propose that
this X-ray source, RX J1836.2+5925, is a rotation-powered gamma-ray pulsar
which is either older or more distant than the prototype Geminga. We see
marginal evidence for variability between two ROSAT HRI observations. If real,
this would indicate that the X-ray emission has an external origin, perhaps due
to intermittent heating of the polar caps by a variable particle accelerator.
RX J1836.2+5925 could even be an old, recycled pulsar, which may nevertheless
have a high gamma-ray efficiency.
