We present multiwavelength photometry and spectroscopy of SN 2022jli, an unprecedented Type Ic supernova discovered in the galaxy NGC 157 at a distance of ≈ 23 Mpc. The multiband light curves reveal many remarkable characteristics. Peaking at a magnitude of g = 15.11 ± 0.02, the high-cadence photometry reveals periodic undulations of 12.5 ± 0.2 days superimposed on the 200-day supernova decline. This periodicity is observed in the light curves from nine separate filter and instrument configurations with peak-to-peak amplitudes of ≃ 0.1 mag. This is the first time that repeated periodic oscillations, over many cycles, have been detected in a supernova light curve. SN 2022jli also displays an extreme early excess that fades over ≈25 days, followed by a rise to a peak luminosity of L opt = 1042.1 erg s−1. Although the exact explosion epoch is not constrained by data, the time from explosion to maximum light is ≳ 59 days. The luminosity can be explained by a large ejecta mass (M ej ≈ 12 ± 6 M ⊙) powered by 56Ni, but we find it difficult to quantitatively model the early excess with circumstellar interaction and cooling. Collision between the supernova ejecta and a binary companion is a possible source of this emission. We discuss the origin of the periodic variability in the light curve, including interaction of the SN ejecta with nested shells of circumstellar matter and neutron stars colliding with binary companions.