We present extensive multicolor (UBVRCIC) photometry of the optical afterglow of GRB 980519. Upon discovery, 8.3 hr after the burst, the source was decaying as a power law, (t - tGRB)α, with a rapid decay rate α1 = -1.73 + 0.04. About 13 hr after the burst a steepening of the light curve to α2 = -2.22 ± 0.04 was observed. Within the framework of current afterglow models, we argue that the rapid initial decline, the " break " in the light curve, and the spectral properties of the afterglow are best interpreted as being due to a collimated ultrarelativistic jet of fixed opening angle expanding into an inhomogeneous medium. In this scenario, we find that the circumburst medium has a density structure that goes as r-2.05 ± 0.22. This is characteristic of a preexisting wind expelled from a massive star. A possible physical scenario is that the progenitor star collapsed to form a black hole (i.e., a " collapsar "), producing the observed burst and afterglow. However, the supernova signature expected in the light curve in such a scenario is not detected. This either implies that the redshift of GRB 980519 is greater than 1.5 or that supernovae accompanying GRBs are not standard candles.