Today’s electronic technology – the pixels on the screen and the process to print the words on the page – are all made possible by the controlled motion of an electron’s charge. In the last decade, the discovery of topological band insulators with robust spin-polarized surface states has launched a new subfield of physics promising a new paradigm in computing. When topology is combined with strong electron correlations, even more interesting states of matter can arise, suggesting additional applications in quantum computing. Here we present the first direct proof of a strongly correlated topological insulator. Using scanning tunneling microscopy to probe the real and momentum space structure of SmB6, we quantify the opening of a Kondo insulating gap. Within that gap, we discover linearly dispersing surface states with the heaviest observed Dirac states in any material – hundreds of times the mass of a free electron. We show how single atom defects can scatter these surface states, and we take the first steps towards manipulating single atoms and thus controlling surface states and their excitations at the nanoscale.