Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications1, 2, 3, 4, 5, 6, 7. Unlike conventional two-dimensional electron states, these surface states are expected to be immune to localization and to overcome barriers caused by material imperfection8, 9, 10, 11, 12, 13, 14. Previous experiments have demonstrated that topological surface states do not backscatter between equal and opposite momentum states, owing to their chiral spin texture15, 16, 17, 18. However, so far there is no evidence that these states in fact transmit through naturally occurring surface defects. Here we use a scanning tunnelling microscope to measure the transmission and reflection probabilities of topological surface states of antimony through naturally occurring crystalline steps separating atomic terraces. In contrast to non-topological surface states of common metals (copper, silver and gold)19, 20, 21, 22, 23, which are either reflected or absorbed by atomic steps, we show that topological surface states of antimony penetrate such barriers with high probability. This demonstration of the extended nature of antimony’s topological surface states suggests that such states may be useful for high current transmission even in the presence of atomic-scale irregularities—an electronic feature sought to efficiently interconnect nanoscale devices.