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 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.