As part of a search for small-scale spectrally anomalous regions within the Mars Global Surveyor Thermal Emission Spectrometer (MGS/TES) data set, we have identified a region ~100 km in diameter on the southwest flanks of the volcano Arsia Mons that exhibits remarkable and persistent water ice cloud cover. High-opacity clouds (by Martian standards) occur in this region in all of the 400 TES spectra covering this area, regardless of season, as well as in all of the MGS Wide-Angle camera images of this same region. We have also found evidence for similar persistent cloudiness at other local solar times of day in this region based on Hubble Space Telescope UV imaging. Modeling of the TES spectra identifies the clouds as water ice and reveals average IR cloud optical depths near 0.5 and typical cloud particle sizes of ~3 ¿m. The presence of persistent cloudiness in this area, even during the relatively warm and cloud-free season near perihelion, may indicate unique local circulation processes, perhaps related to orographic effects or the interaction between the global circulation and the Tharsis region in general. Our analysis also demonstrates that through careful modeling it is possible to extend the search for unique spectral features in the TES data far into the wings of the strong 15-¿m CO2 band.