  We present multi-wavelength photometry and spectroscopy of SN 2022jli, an
unprecedented Type Ic supernova discovered in the galaxy NGC 157 at a distance
of $\approx$ 23 Mpc. The multi-band light curves reveal many remarkable
characteristics. Peaking at a magnitude of $g=15.11\pm0.02$, the high-cadence
photometry reveals 12.5$\pm0.2\ $day periodic undulations 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 $\simeq$ 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 which fades over $\approx$ 25
days followed by a rise to a peak luminosity of $L_{\rm opt} = 10^{42.1}$ erg
s$^{-1}$. Although the exact explosion epoch is not constrained by data, the
time from explosion to maximum light is $\gtrsim$ 59 days. The luminosity can
be explained by a large ejecta mass ($M_{\rm ej}\approx12\pm6$M$_{\odot}$)
powered by $^{56}$Ni but we find difficulty in quantitatively modelling 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.
