  The brightest Fast Blue Optical Transients (FBOTs) are mysterious
extragalactic explosions that may represent a new class of astrophysical
phenomena. Their fast time to maximum brightness of less than a week and
decline over several months and atypical optical spectra and evolution are
difficult to explain within the context of core-collapse of massive stars which
are powered by radioactive decay of Nickel-56 and evolve more slowly. AT2018cow
(at redshift of 0.014) is an extreme FBOT in terms of rapid evolution and high
luminosities. Here we present evidence for a high-amplitude quasi-periodic
oscillation (QPO) of AT2018cow's soft X-rays with a frequency of 224 Hz (at
3.7$\sigma$ significance level or false alarm probability of 0.02%) and
fractional root-mean-squared amplitude of >30%. This signal is found in the
average power density spectrum taken over the entire 60-day outburst and
suggests a highly persistent signal that lasts for a billion cycles. The high
frequency (rapid timescale) of 224 Hz (4.4 ms) argues for a compact object in
AT2018cow, which can be a neutron star or black hole with a mass less than 850
solar masses. If the QPO is the spin period of a neutron star, we can set
limits on the star's magnetic field strength. Our work highlights a new way of
using high time-resolution X-ray observations to study FBOTs.
