A novel experimental technique to measure the energy-dependent unimolecular dissociation rate k(E) of radical species is presented. Internally-excited CH3CO radicals were formed by ultraviolet photodissociation of CH3COCl, and the subsequent decay of these radicals was detected by subpicosecond time-clocked photofragment imaging. The CH3CO radicals with different internal energies were dispersed in space by their recoil velocities, and their decay rates were measured for each internal energy. The dissociation rates of CH3CO radicals determined were an order of magnitude smaller than those calculated by Rice-Ramsperger-Kassel-Marcus theory.