The brightest fast blue optical transients (FBOTs) are mysterious extragalactic explosions that may represent a new astrophysical phenomenon(1). Their fast time to maximum brightness of less than a week, decline over several months, and atypical optical spectra and evolution are difficult to explain within the context of the core collapse of massive stars, which are powered by radioactive decay of Ni-56 and evolve more slowly(2,3). AT2018cow (at a redshift of 0.014) is an extreme FBOT in terms of rapid evolution and high luminosity(4-7). Here we present evidence for a high-amplitude quasiperiodic oscillation of AT2018cow's soft X-rays with a frequency of 224 Hz (at a 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 could be a neutron star or black hole with a mass less than 850 solar masses. If the quasiperiodic oscillation is equivalent to 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.