One of the unsolved mysteries of gamma-ray astronomy concerns the nature of the unidentified gamma-ray sources. Recently, using the Second Fermi LAT source catalog (2FGL) and the Wide-field Infrared Survey Explorer (WISE) archive, we discovered that the WISE counterparts of gamma-ray blazars, a class of active galactic nuclei, delineate a region (the WISE Gamma-ray Strip) in the 3- dimensional infrared color space well separated from the locus of the other astronomical objects. Based on this result, we built an association procedure to recognize if there are WISE blazar candidates within the positional uncertainty region of the unidentified gamma-ray sources. Here we report on our analysis of 2FGL J1823.8+4312, a gamma-ray active galactic nucleus of uncertain type associated with the X-ray source 1RXS J182418.7+430954 according to the 2FGL, to verify whether it is a blazar. Applying our association method we found two sources with IR colors typical of gamma-ray blazars, located within the 99.9% confidence region of 2FGL J1823.8+4312: WISE J182352.33+431452.5 and WISE J182409.25+431404.7. Then we searched in the Chandra, NVSS and SDSS archival observations for their counterparts. We discovered that WISE J182352.33+431452.5, our preferred gamma-ray blazar candidate according to our WISE association procedure, is detected in the optical and in the X-rays but not in the radio, making it extremely unusual if it is a blazar. Given its enigmatic spectral energy distribution, we considered the possibility that it is a radio faint blazar or the prototype of a new class of extragalactic sources, our conclusion is independent of whether WISE J182352.33+431452.5 is the actual counterpart of 2FGL J1823.8+4312. Show Partial Abstract