In 2005, Kane and Mele [Phys. Rev. Lett. 95, 226801 (2005)] predicted that at sufficiently low energy, graphene exhibits a topological state of matter with an energy gap generated by the atomic spin-orbit interaction. However, this intrinsic gap has not been measured to this date. In this Letter, we exploit the chirality of the low-energy states to resolve this gap. We probe the spin states experimentally by employing low temperature microwave excitation in a resistively detected electron-spin resonance on graphene. The structure of the topological bands is reflected in our transport experiments, where our numerical models allow us to identify the resonance signatures. We determine the intrinsic spin-orbit bulk gap to be exactly 42.2 μeV. Electron-spin resonance experiments can reveal the competition between the intrinsic spin-orbit coupling and classical Zeeman energy that arises at low magnetic fields and demonstrate that graphene remains to be a material with surprising properties.