The EGRET telescope aboard NASAs Compton GRO has repeatedly detected 3EG J1835+5918, a bright and steady source of high-energy gamma-ray emission with no identification suggested until recently. The long absence of any likely counterpart for a bright gamma-ray source located 25 degrees off the Galactic plane initiated several attempts of deep observations at other wavelengths. We report on counterparts in X-rays on a basis of a 60 ksec ROSAT HRI image. In order to conclude on the plausibility of the X-ray counterparts, we reanalyzed data from EGRET at energies above 100 MeV and above 1 GeV, including data up to CGRO observation cycle 7. The gamma-ray source location represents the latest and probably the final positional assessment based on EGRET data. The X-ray counterparts were studied during follow-up optical identification campaigns, leaving only one object to be likely associated with the gamma-ray source 3EG J1835+5918. This object, RX J1836.2+5925, has the characteristics of an isolated neutron star and possibly of a radio-quiet pulsar.