The prediction and subsequent discovery of robust spin-polarized surface states on topological band insulators has launched a new subfield of physics over the last decade. In the last few years it has been recognized that when topology is combined with strong electron-electron correlations, even more interesting and potentially useful states of matter can arise, such as new topological classifications, fractionalized states, and many-body localization that preserves the topology of the insulating state against thermal destruction. Here we show the first direct proof of a strongly correlated topological insulator. Using scanning tunneling microscopy to probe real and momentum space structure, our measurements on the heavy fermion material SmB6 reveal the evolution of the insulating gap arising from strong interactions. Within the narrow gap, we directly image a dispersing surface state that converges to a Dirac point close to the chemical potential. Our observations present the first opportunity to explore a strongly correlated topological state of matter.