gamma-ray bursts (GRBs) have puzzled astronomers for almost three decades, primarily owing to the lack of identifications at other wavelengths. The detection of a radio counterpart(1) enables application of the powerful technique of very long baseline interferometry (VLBI) to this intriguing class of objects. Here we present VLBI monitoring of VLA J065349.4 + 791619 obtained between 8 and 25 days after the initial gamma-ray burst. The radio emission is found to be very compact, with an angular extent of less than 1 milliarcsecond. We derive a position for the radio counterpart accurate to 200 microarcseconds, and constrain the proper motion of VLA J065349.4 + 791619 be less than 50 milliarcseconds per year. We place an upper limit on the annual parallax of 1 milliarcsecond. These results are entirely consistent with the expectations of cosmological models.