Topological superconductivity is an exotic state of matter that supports Majorana zero-modes, which have been predicted to occur in the surface states of three-dimensional systems, in the edge states of two-dimensional systems, and in onedimensional wires(1,2). Localized Majorana zero-modes obey non-Abelian exchange statistics, making them interesting building blocks for topological quantum computing(3,4). Here, we report superconductivity induced in the edge modes of semiconducting InAs/GaSb quantum wells, a two-dimensional topological insulator(5-10). Using superconducting quantum interference we demonstrate gate-tuning between edge-dominated and bulk-dominated regimes of superconducting transport. The edge-dominated regime arises only under conditions of high-bulk resistivity, which we associate with the two-dimensional topological phase. These experiments establish InAs/GaSb as a promising platform for the confinement of Majoranas into localized states, enabling future investigations of non-Abelian statistics.