Using Subaru/Suprime-Cam wide-field imaging and both Keck/ESI and LBT/MODS spectroscopy, we identify and characterize a compact star cluster, which we term NGC 3628-UCD1, embedded in a stellar stream around the spiral galaxy NGC 3628. The size and luminosity of UCD1 are similar to $omega$ Cen, the most luminous Milky Way globular cluster, which has long been suspected to be the stripped remnant of an accreted dwarf galaxy. The object has a magnitude of $i=19.3$ mag (${rm L}_{rm i}=1.4times10^{6}~{rm L}_{odot}$). UCD1 is marginally resolved in our ground-based imaging, with a half-light radius of $sim10$ pc. We measure an integrated brightness for the stellar stream of $i=13.1$ mag, with $(g-i)=1.0$. This would correspond to an accreted dwarf galaxy with an approximate luminosity of ${rm L}_isim4.1times10^{8}~{rm L}_{odot}$. Spectral analysis reveals that UCD1 has an age of $6.6$ Gyr , $[rm{Z}/rm{H}]=-0.75$, an $[{alpha}/rm{Fe}]=-0.10$. We propose that UCD1 is an example of an $omega$ Cen-like star cluster possibly forming from the nucleus of an infalling dwarf galaxy, demonstrating that at least some of the massive star cluster population may be created through tidal stripping.