Spin currents which allow for a dissipationless transport of information can be generated by electric fields in semiconductor heterostructures in the presence of a Rashba-type spin-orbit coupling. The largest Rashba effects occur for electronic surface states of metals but these cannot exist but under ultrahigh vacuum conditions. Here, we reveal a giant Rashba effect ({alpha}_R ~ 1.5E-10 eVm) on a surface state of Ir(111). We demonstrate that its spin splitting and spin polarization remain unaffected when Ir is covered with graphene. The graphene protection is, in turn, sufficient for the spin-split surface state to survive in ambient atmosphere. We discuss this result along with evidences for a topological protection of the surface state.