The reactivity of 1,2,3 butatriene, C4H4, has been postulated to be due to the presence of low-lying triplet states. However, there have been no experimental or theoretical determinations of the energy separations or geometries of these states. We have examined the structures, energetics, and possible mechanisms involved in the self-polymerization of the title compound using single-determinant ab initio molecular orbital theory. We find that the magnitude of the singlet-triplet gap for the monomer and its relatively high positive heat of formation does not allow for a mechanism involving the direct formation of an isolated triplet species. We speculate on an alternative mechanism and show its relationship to recent work on related reactive monomers.