The existence of topological superconductors preserving time-reversal symmetry was recently predicted, and they are expected to provide a solid-state realization of itinerant massless Majorana fermions and a route to topological quantum computation. Their first likely example, Cu[subscript x]Bi[subscript 2]Se[subscript 3], was discovered last year, but the search for new materials has so far been hindered by the lack of a guiding principle. Here, we report point-contact spectroscopy experiments suggesting that the low-carrier-density superconductor Sn[subscript 1-x]In[subscript x]Te is accompanied by surface Andreev bound states which, with the help of theoretical analysis, would give evidence for odd-parity pairing and topological superconductivity. The present and previous finding of possible topological superconductivity in Sn[subscript 1-x]In[subscript x]Te and Cu[subscript x]Bi[subscript 2]Se[subscript 3] suggests that odd-parity pairing favored by strong spin-orbit coupling is likely to be a common underlying mechanism for materializing topological superconductivity.United States. Air Force Office of Scientific Research (AOARD 124038)