Mössbauer-effect and microwave absorption experimental evidence unambiguously demonstrates the presence of slow, approximately 450 MHz, tunneling of magnetic europium between four equivalent sites in Eu8Ga16Ge30, a stoichiometric clathrate. Remarkably, six of the eight europium atoms, or 11% of the constituents in this solid, tunnel between these four sites separated by 0.55 A. The off centering of the atoms or ions in crystalline clathrates appears to be a promising route for producing Rabi oscillators in solid-state materials.