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Of the more than $3{,}000$ radio pulsars currently known, only ${\sim}300$ are in binary systems, and only five of these consist of young pulsars with massive non-degenerate companions. We present the discovery and initial timing, accomplished using the Canadian Hydrogen Intensity Mapping Experiment telescope (CHIME), of the sixth such binary pulsar, PSR J2108+4516, a $0.577$-s radio pulsar in a 269-day orbit of eccentricity 0.09 with a companion of minimum mass $11$ M$_{\odot}$. Notably, the pulsar undergoes periods of substantial eclipse, disappearing from the CHIME $400{-}800$ MHz observing band for a large fraction of its orbit, and displays significant dispersion measure and scattering variations throughout its orbit, pointing to the possibility of a circumstellar disk or very dense stellar wind associated with the companion star. Subarcsecond resolution imaging with the Karl G. Jansky Very Large Array unambiguously demonstrates that the companion is a bright, $V \simeq 11$ OBe star, EM* UHA 138, located at a distance of $3.26(14)$ kpc. Archival optical observations of \companion{} approximately suggest a companion mass ranging from $17.5$ M$_{\odot} < M_{\rm c} < 23$ M$_{\odot}$, in turn constraining the orbital inclination angle to $50.3^{\circ} \lesssim i \lesssim 58.3^{\circ}$. With further multi-wavelength followup, PSR J2108+4516 promises to serve as another rare laboratory for the exploration of companion winds, circumstellar disks, and short-term evolution through extended-body orbital dynamics.