A computational study of the reaction of P+(P-3) with acetylene has been carried out. The only exothermic products correlating with the reactants are PCCH+((2)Pi) + H(S-2). Two different pathways leading to these products that are apparently barrier-free have been found. Both pathways involve isomerization into open-chain intermediates followed by direct elimination of a hydrogen atom. The possibility of spin-crossing has been considered because the species on the singlet surface are considerably more stable than those on the triplet one. On the singlet surface, there are other possible channels for the reaction, namely, cyclic PC2H+((2)A') + H(S-2) and CCP+((1)Sigma) + H-2 ((1)Sigma(+)(g)). A computational kinetic study shows that, in agreement with the experimental evidence, the major products are PCCH+((2)Pi) + H(S-2) at all temperatures. Only at very high temperatures is CCP+((1)Sigma) + H-2 ((1)Sigma(+)(g)) formed in non-negligible amounts. Therefore, only PCCH+ should be formed in the interstellar medium.