Topological insulators host spin-polarized surface states which robustly span the band gap and hold promise for novel applications. Recent theoretical predictions have suggested that topologically protected surface states may similarly span the hybridization gap in some strongly correlated heavy fermion materials, particularly SmB6. However, the process by which the Sm 4f electrons hybridize with the 5d electrons on the surface of SmB6, and the expected Fermi-level gap in the density of states out of which the predicted topological surface states must arise, have not been directly measured. We use scanning tunneling microscopy to conduct the first atomic resolution spectroscopic study of the cleaved surface of SmB6, and to reveal a robust hybridization gap which universally spans the Fermi level on four distinct surface morphologies despite shifts in the f band energy. Using a cotunneling model, we separate the density of states of the hybridized bands from which the predicted topological surface states must be disentangled. On all surfaces we observe residual spectral weight spanning the hybridization gap down to the lowest T, which is consistent with a topological surface state.