We present broadband radio observations spanning 1.4-350 GHz of the aftergl
ow of GRB 991216, taken 1-80 days after the burst. The optical and X-ray af
terglow of this burst were fairly typical and are explained by a jet fireba
ll. In contrast, the radio afterglow is unusual in two respects: (1) the ra
dio light curve does not show the usual rise to maximum flux on timescales
of weeks and instead appears to be declining already on day I; and (2) the
power-law indices show significant steepening from the radio through the X-
ray bands. We show that the standard fireball model, in which the afterglow
is from a forward shock, is unable to account for point 1, and we conclude
that the bulk of the radio emission must arise from a different source. We
consider two models, neither of which can be ruled out with the existing d
ata. In the first (conventional) model, the early radio emission is attribu
ted to emission from the reverse shock, as in the case of GRB 990123. In th
e second "dual fireball" model, the radio emission originates from the forw
ard shock of an isotropically energetic fireball (10(54) ergs) expanding in
to a tenuous medium (10(-4) cm(-3)), while the optical and X-ray emission o
riginate in a jetlike outflow. Finally, we note that the near-IR bump of th
e afterglow is similar to that seen in GRB 971214, and no fireball model ca
n explain this bump.