In addition to a bulk energy gap, topological insulators accommodate a conducting, linearly dispersed Dirac surface state. This state is predicted to become massive if time reversal symmetry is broken, and to become insulating if the Fermi energy is positioned inside both the surface and bulk gaps. We introduced magnetic dopants into the three-dimensional topological insulator dibismuth triselenide (Bi₂Se₃) to break the time reversal symmetry and further position the Fermi energy inside the gaps by simultaneous magnetic and charge doping. The resulting insulating massive Dirac fermion state, which we observed by angle-resolved photoemission, paves the way for studying a range of topological phenomena relevant to both condensed matter and particle physics.