This Letter introduces a new technique to probe the competing unimolecular dissociation channels of isomerically-selected hydrocarbon radicals as a function of internal energy in the radical. The crossed laser-molecular beam scattering experiments produce 2-propenyl radicals by photolysis of 2-chloropropene and disperse the radicals by the neutral velocity imparted in the photolysis; thus dispersing them by internal energy in the neutral time-of-flight spectrum. For the unstable radicals, the experiments then measure the branching between the two competing C-H bond fission product channels via tunable vacuum-UV photoionization of the products. Dispersing the neutral products by arrival time at the detector allows us to measure the branching between isomeric product channels as a function of internal energy in the dissociating radical isomer. The data resolve the competition between the unimolecular H + allene and H + propyne product channels from the radical with internal energies from 0 to 18 kcal/mol above the H + propyne barrier. We find that the barrier to H + allene formation from this high-energy C3H5 radical is slightly higher than the barrier to H + propyne formation, in agreement with recent theoretical calculations but in sharp contrast to that predicted for the most stable C3H5 isomer, the allyl radical. The dominance of the branching to H + propyne formation over H + allene formation for this isomer persists at the higher internal energies in agreement with RRKM predictions that take into account the freezing of the methyl rotor in the H + allene channel and predict a concomitant reduction in the A factor for that channel.