We discuss the nature of the unidentified EGRET source 3EG J1621+8203. In an effort to identify the gamma-ray source, we have examined X-ray images of the field from ROSAT PSPC, ROSAT HRI, and ASCA GIS. Of the several faint X-ray point sources in the error circle of 3EG J1621+8203, most are stars or faint radio sources, unlikely to be counterparts to the EGRET source. The most notable object in the gamma-ray error box is the bright FR I radio galaxy NGC 6251. If 3EG J1621+8203 corresponds to NGC 6251, then it would be the second radio galaxy to be detected in high-energy gamma rays after Cen A, which provided the first clear evidence of the detection above 100 MeV of an active galactic nucleus (AGN) with a large-inclination jet. If the detection of more radio galaxies by EGRET has been limited by its threshold sensitivity, there exists the exciting possibility that new high-energy gamma-ray instruments, with much higher sensitivity, will detect a larger number of radio galaxies in the future.