Lobate features abutting massifs and escarpments in the middle latitudes of Mars have been recognized in images for decades, but their true nature has been controversial, with hypotheses of origin such as ice-lubricated debris flows or glaciers covered by a layer of surface debris. These models imply an ice content ranging from minor and interstitial to massive and relatively pure. Soundings of these deposits in the eastern Hellas region by the Shallow Radar on the Mars Reconnaissance Orbiter reveal radar properties entirely consistent with massive water ice, supporting the debris-covered glacier hypothesis. The results imply that these glaciers formed in a previous climate conducive to glaciation at middle latitudes. Such features may collectively represent the most extensive nonpolar ice yet recognized on Mars.