When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect1, 2 dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin–orbit interactions may also naturally support conducting topological boundary states in the quantum limit3, 4, 5, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields6. Bulk Bi1-xSbx single crystals are predicted to be prime candidates7, 8 for one such unusual Hall phase of matter known as the topological insulator9, 10, 11. The hallmark of a topological insulator is the existence of metallic surface states that are higher-dimensional analogues of the edge states that characterize a quantum spin Hall insulator3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. In addition to its interesting boundary states, the bulk of Bi1-xSbx is predicted to exhibit three-dimensional Dirac particles14, 15, 16, 17, another topic of heightened current interest following the new findings in two-dimensional graphene18, 19, 20 and charge quantum Hall fractionalization observed in pure bismuth21. However, despite numerous transport and magnetic measurements on the Bi1-xSbx family since the 1960s17, no direct evidence of either topological Hall states or bulk Dirac particles has been found. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES), we report the direct observation of massive Dirac particles in the bulk of Bi0.9Sb0.1, locate the Kramers points at the sample's boundary and provide a comprehensive mapping of the Dirac insulator's gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the 'topological metal'9, 10, 11. They also suggest that this material has potential application in developing next-generation quantum computing devices that may incorporate 'light-like' bulk carriers and spin-textured surface currents.