We present optical photometry and spectroscopy of SN 2019stc (=ZTF19acbonaa), an unusual Type Ic supernova (SN Ic) at a redshift of z=0.117. SN 2019stc exhibits a broad double-peaked light curve, with the first peak having an absolute magnitude of M_r_=-20.0mag, and the second peak, about 80 rest-frame days later, M_r_=-19.2mag. The total radiated energy is large, E_rad_~2.5x10^50^erg. Despite its large luminosity, approaching those of Type I superluminous supernovae (SLSNe), SN 2019stc exhibits a typical SN Ic spectrum, bridging the gap between SLSNe and SNe Ic. The spectra indicate the presence of Fe-peak elements, but modeling of the first light-curve peak with radioactive heating alone leads to an unusually high nickel mass fraction of f_Ni_~0.31 (M_Ni_~3.2M_{sun}). Instead, if we model the first peak with a combined magnetar spin-down and radioactive heating model we find a better match with M_ej~4M_{sun}, a magnetar spin period of P_spin~7.2ms, and magnetic field of B~10^14^G, and f_Ni_<~0.2 (consistent with SNe Ic). The prominent second peak cannot be naturally accommodated with radioactive heating or magnetar spin-down, but instead can be explained as circumstellar interaction with ~0.7M_{sun} of hydrogen-free material located ~400au from the progenitor. Accounting for the ejecta mass, circumstellar shell mass, and remnant neutron star mass, we infer a CO core mass prior to explosion of ~6.5M{sun}. The host galaxy has a metallicity of ~0.26Z{sun}_, low for SNe Ic but consistent with SLSNe. Overall, we find that SN 2019stc is a transition object between normal SNe Ic and SLSNe.