This Letter reports experimental results on the three-wave interactions of backward volume spin waves in a magnetic film and the excitation of chaotic waves through such interactions in a magnetic film-based active feedback ring. The three-wave interactions manifest themselves in the power saturation responses of spin waves, and the chaotic excitation manifests itself in chaotic waveforms and broad spectra. The fractal dimensions of the chaotic signals are finite and can be controlled by changing the ring gain.