We report the observation of strong coupling of a macroscopic ensemble of ~10^{16} Fe_8 molecular nanomagnets to the resonant mode of a microwave cavity. We use millimeter-wave spectroscopy to measure the splitting of the system's resonant frequency induced by the coupling between the spins and the cavity mode. The magnitude of this splitting is found to scale with Sqrt[N], where N is the number of collectively coupled spins. We control N by changing the system's temperature and, thereby, the populations of the relevant spin energy levels. Strong coupling is observed for two distinct transitions between spin energy states. Our results indicate that at low temperatures nearly all of the spins in the sample couple with the cavity's resonant mode even though there is substantial inhomogeneous broadening of the Fe8 spin resonances. ; Comment: Main text: 12 pages, including 3 figures. Supplement: 5 pages, including 2 figures. 17 pages total