The interplay between strong electron interactions and band topology is a new frontier in the search for exotic quantum phases. The Kondo insulator SmB6 has emerged as a promising platform because its correlation-driven bulk gap is predicted to host topological surface modes entangled with f electrons, spawning heavy Dirac fermions1-4. Unlike the conventional surface states of non-interacting topological insulators, heavy Dirac fermions are expected to harbour spontaneously generated quantum anomalous Hall states5, non-Abelian quantum statistics6,7, fractionalization8 and topological order6-8. However, the small energy scales required to probe heavy Dirac fermions have complicated their experimental realization. Here we use high-energy-resolution spectroscopic imaging in real and momentum space on SmB6. On cooling below 35 K, we observe the opening of an insulating gap that expands to 14 meV at 2 K. Within the gap, we image the formation of linearly dispersing surface states with effective masses reaching 410 ± 20 me (where me is the mass of the electron). Our results demonstrate the presence of correlation-driven heavy surface states in SmB6, in agreement with theoretical predictions1-4. Their high effective mass translates to a large density of states near zero energy, which magnifies their susceptibility to the anticipated novel orders and their potential utility.