Realization of the quantum spin Hall effect in graphene devices has remained an outstanding challenge dating back to the inception of the field of topological insulators. Graphene's exceptionally weak spin-orbit coupling-stemming from carbon's low mass-poses the primary obstacle. We experimentally and theoretically study artificially enhanced spin-orbit coupling in graphene via random decoration with dilute Bi2Te3 nanoparticles. Multiterminal resistance measurements suggest the presence of helical edge states characteristic of a quantum spin Hall phase; the magnetic field and temperature dependence of the resistance peaks, x-ray photoelectron spectra, scanning tunneling spectroscopy, and first-principles calculations further support this scenario. These observations highlight a pathway to spintronics and quantum information applications in graphene-based quantum spin Hall platforms.