We present multifrequency radio observations from the afterglow of GRB 980519 beginning 7.2 hr after the gamma-ray burst and ending 63 days later. The fast decline in the optical and X-ray light curves for this burst has been interpreted either as afterglow emission originating from a collimated outflow-a jet-or the result of a blast wave propagating into a medium whose density is shaped by the wind of an evolved massive star. These two models predict divergent behavior for the radio afterglow, and therefore radio observations are capable, in principle, of discriminating between the two. We show that a wind model describes the subsequent evolution of the radio afterglow rather well. However, we see strong modulation of the light curve, which we interpret as diffractive scintillation. These variations prevent us from decisively rejecting the jet model.