The temporal evolution of fluorescence from isolated single-wall carbon nanotubes (SWNTs) has been investigated using optical Kerr gating. The fluorescence emission is found to decay on a time scale of 10 ps. This fast relaxation arises from nonradiative processes, the existence of which explains the relatively low observed fluorescence efficiency in isolated SWNTs. From the measured decay rate and a determination of fluorescence quantum efficiency, we deduce a radiative lifetime of 110 ns.