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 Mr = -20.0 mag, and the second peak, about 80 rest-frame days later, Mr = -19.2 mag. The total radiated energy is large, Erad ≈ 2.5 × 1050 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 fNi ≈ 0.31 (MNi ≈ 3.2 M⊙). Instead, if we model the first peak with a combined magnetar spin-down and radioactive heating model we find a better match with Mej ≈ 4 M⊙, a magnetar spin period of Pspin ≈ 7.2 ms, and magnetic field of B ≈ 1014 G, and fNi ≲ 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 ≈0.7 M⊙ of hydrogen-free material located ≈400 au 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 ≈6.5 M⊙. The host galaxy has a metallicity of ≈0.26 Z⊙, low for SNe Ic but consistent with SLSNe. Overall, we find that SN 2019stc is a transition object between normal SNe Ic and SLSNe.