Abstract We report on VLBI observations of the fast and blue optical transient (FBOT), AT 2018cow. At ∼62 Mpc, AT 2018cow is the first relatively nearby FBOT. The nature of AT 2018cow is not clear, although various hypotheses from a tidal disruption event to different kinds of supernovae have been suggested. It had a very fast rise time (3.5 d) and an almost featureless blue spectrum although high photospheric velocities (40,000 km s−1) were suggested early on. The X-ray luminosity was very high, ∼1.4 × 1043 erg s−1, larger than those of ordinary SNe, and more consistent with those of SNe associated with gamma-ray bursts. Variable hard X-ray emission hints at a long-lived “central engine.” It was also fairly radio luminous, with a peak 8.4-GHz spectral luminosity of ∼4 × 1028 erg s−1 Hz−1, allowing us to make VLBI observations at ages between 22 and 287 d. We do not resolve AT 2018cow. Assuming a circularly symmetric source, our observations constrain the average apparent expansion velocity to be <0.49 c by t = 98 d (3σ limit). We also constrain the proper motion of AT 2018cow to be <0.51 c. Since the radio emission generally traces the fastest ejecta, our observations make the presence of a long-lived relativistic jet with a lifetime of more than one month very unlikely.