We present optical observations of supernova SN 2014C, which underwent an unprecedented slow metamorphosis from H-poor type Ib to H-rich type IIn over the course of one year. The observed spectroscopic evolution is consistent with the supernova having exploded in a cavity before encountering a massive shell of the progenitor star's stripped hydrogen envelope. Possible origins for the circumstellar shell include a brief Wolf-Rayet fast wind phase that overtook a slower red supergiant wind, eruptive ejection, or confinement of circumstellar material by external influences of neighboring stars. An extended high velocity Hα absorption feature seen in near-maximum light spectra implies that the progenitor star was not completely stripped of hydrogen at the time of core collapse. Archival pre-explosion Subaru Telescope Suprime-Cam and Hubble Space Telescope Wide Field Planetary Camera 2 images of the region obtained in 2009 show a coincident source that is most likely a compact massive star cluster in NGC 7331 that hosted the progenitor system. By comparing the emission properties of the source with stellar population models that incorporate interacting binary stars we estimate the age of the host cluster to be 30-300 Myr, and favor ages closer to 30 Myr in light of relatively strong Hα emission. SN 2014C is the best observed member of a class of core-collapse supernovae that fill the gap between events that interact strongly with dense, nearby environments immediately after explosion and those that never show signs of interaction. Better understanding of the frequency and nature of this intermediate population can contribute valuable information about the poorly understood final stages of stellar evolution.