Nuclear spins of noble gases can maintain coherence for hours at ambient conditions owing to their extraordinary isolation by the enclosing, complete electronic shells. This isolation, however, impedes the ability to manipulate and control them by optical means or by physical coupling to other spin gases. Here we experimentally achieve strong coherent coupling between noble-gas spins and the optically-accessible spins of alkali-metal vapor. Stochastic spin-exchange collisions, underlying the coupling, accumulate to a coherent periodic exchange of spin excitations between the two gases. We obtain a coupling rate 10 times higher than the decay rate, observe the resultant avoided crossing in the spectral response of the spins, and demonstrate the external control over the coupling by magnetic fields. These results open a route for efficient and rapid interfacing with noble-gas spins for applications in quantum sensing and information.