  We report on a comprehensive radio monitoring program of the bright gamma-ray
burster GRB970111. These VLA observations were made at a frequency of 1.4 GHz
and span a range of post-burst timescales between 28 hours and one month.
Despite extensive sampling at sub-milliJansky sensitivities, no radio source
was detected above 0.5 mJy in the current best error box (~14 arcmin^2) for
GRB970111. A highly unusual radio source, VLA J1528.7+1945, was seen to drop in
flux density by a factor of two in our monitoring period but it lies outside
the error box and thus it is unlikely to be related to GRB970111. Cosmological
fireball models of gamma-ray bursts make predictions of late-time emission
occurring at longer wavelengths. The absence of a flaring or fading radio
counterpart to GRB970111 provides strong constraints on these models.
