Topological insulators (TI) are a phase of matter that host unusual metallic surface states. Unlike the states that exist on the surface of conventional materials, these so-called topological surfaces states (TSS) are protected against disorder-related localization effects by time reversal symmetry through strong spin-orbit coupling. By combining transport measurements, angle-resolved photoemission spectroscopy, and scanning tunneling microscopy, we show that there exists a critical level of disorder beyond which the TI loses its ability to protect the metallic TSS and transitions to a fully insulating state. The absence of the metallic surface channels dictates that there is a change in the material's topological character, implying that disorder can lead to a topological phase transition even without breaking the time reversal symmetry. This observation challenges the conventional notion of topologically protected surface states and should prompt new studies as to the fundamental nature of topological phase of matter in the presence of disorder.