Geomorphological features potentially related to subsurface ice, such as scalloped depressions, expanded craters, pedestal craters, and banded terrain, are present in and around Hellas Planitia, Mars. We present a radar survey of the region using the Shallow Radar (SHARAD) instrument on board the Mars Reconnaissance Orbiter (MRO) to identify candidate subsurface reflectors that may be due to the presence of potentially ice-rich deposits. We found that the majority of radar returns are likely from off-nadir surface topography ("clutter"), arising from the rough topography of the region. There is no widespread radar return from any subsurface interfaces. However, we identify a group of six reflectors adjacent to each other on a plateau in Malea Patera in which we have higher confidence. Landforms associated with a likely ice-rich mantle are associated with the plateau, but the thickness of this mantle does not correspond to the expected depth of the reflectors. However, layers beneath the mantle and marginal pitting at the edge of the plateau are similar to those associated with pedestal craters, which may be ice rich and are a similar thickness to the expected depth of the reflectors. Malea Patera has been interpreted to be a volcanic caldera, so the reflectors may be associated with a volcanic deposit within the plateau, although the evidence for this is inconclusive. Because this radar detection is localized and its origin ambiguous, we cannot use it to make conclusions about the thickness of subsurface deposits in the Hellas region as a whole. The lack of widespread radar reflectors in this region, as compared to the northern mid-latitudes where extensive radar reflections have been mapped, may be due in part to higher surface roughness, which creates radar clutter that may obscure subsurface reflectors. However on the southern rim of the basin and south of the basin, the lack of reflectors may indicate that the possible ice-rich deposits observed geomorphologically in this region are too thin to be resolved by SHARAD, are dielectrically similar to the underlying unit, or have a gradual vertical transition in ice content that is not reflective for the radar. This would imply that recent climate processes may have favored widespread, thick ice deposition or preservation in the northern hemisphere as compared to the southern hemisphere.