The ring closure reaction of C4H3 with acetylene to give phenyl radical is one proposed mechanism for the formation of the first aromatic ring in hydrocarbon combustion. There are two low-lying isomers of C4H3; 1-dehydro-buta-1-ene-3-yne (n-C4H3) and 2-dehydro-buta-1-ene-3-yne (iso-C4H3). It has been proposed that only n-C4H3 reacts with acetylene to give phenyl radical, and since iso-C4H3 is more stable than n-C4H3, formation of phenyl radical by this mechanism is unlikely. We report restricted Hartree-Fock (RHF) plus singles and doubles configuration interaction calculations with a Davidson’s correction (RHF+1+2+Q) using the Dunning correlation consistent Polarized valence double zeta basis set (cc-pVDZ) for stationary point structures along the reaction pathway for the reactions of n-C4H3 and iso-C4H3 With acetylene. n-C4H3 plus acetylene (9.4) has a small entrance channel barrier (17.7) (all energetics in parentheses are in kcal/mol with respect to iso-C4H3 plus acetylene) and the subsequent closure steps leading to phenyl radical (-91.9) are downhill with respect to the entrance channel barrier. Iso-C4H3 plus acetylene also has an entrance channel barrier (14.9) and there is a downhill pathway to l-dehydro-fulvene (-55.0). 1-dehydro-fulvene can rearrange to 6-dehydro-fulvene (-60.3) by a 1.3-hydrogen shift over a barrier (4.0), which is still below the entrance channel barrier,from which rearrangement to phenyl radical can occur by a downhill pathway. Thus, both n-C4H3 and iso-C4H3 can react with acetylene to give phenyl radical with small barriers.