The millimeter wavelength emission from GRB 991208 is the second brightest ever detected, yielding a unique data set. We present here well-sampled spectra and light curves over more than two decades in frequency for a 2 week period. This data set has allowed us for the first time to trace the evolution of the characteristic synchrotron self-absorption frequency ν$_a$, peak frequency ν$_m$, and the peak flux density F$_m$; we obtain ν$_a$åisebox-0.5ex t $^-0.15+/-0.23$, ν$_m$i̊sebox-0.5extex tasciitildet$^-1.7+/-0.7$, and F$_m$rs̊ebox-0.5ex t$^-0.47+/-0.20$. From the radio data we find that models of homogeneous or wind- generated ambient media with a spherically symmetric outflow can be ruled out. A model in which the relativistic outflow is collimated (a jet) can account for the observed evolution of the synchrotron parameters, the rapid decay at optical wavelengths, and the observed radio-to-optical spectral flux distributions that we present here, provided that the jet transition has not been fully completed in the first 2 weeks after the event. These observations provide additional evidence that rapidly decaying optical/X-ray afterglows are due to jets and that such transitions either develop very slowly or perhaps never reach the predicted asymptotic decay F(t)rae̊box-0.5ex t$^-p$.