The origin of Saturn's ~26.7° obliquity and ~100-million-year-old rings is unknown. The observed rapid outward migration of Saturn's largest satellite, Titan, could have raised Saturn's obliquity through a spin-orbit precession resonance with Neptune. We use Cassini data to refine estimates of Saturn's moment of inertia, finding that it is just outside the range required for the resonance. We propose that Saturn previously had an additional satellite, which we name Chrysalis, that caused Saturn's obliquity to increase through the Neptune resonance. Destabilization of Chrysalis's orbit ~100 million years ago can then explain the proximity of the system to the resonance and the formation of the rings through a grazing encounter with Saturn.