We have studied the reaction between vinyl and acetylene theoretically using electronic structure theory (DFT-B3LYP and a G2-like method) to calculate properties of stationary points on the potential, RRKM theory to compute microcanonical rate coefficients, and solutions to the time-dependent, multiple-well master equation to extract information about the thermal rate coefficient and product distribution as a function of temperature and pressure. For the temperature range, 300 K less than or equal to T less than or equal to 700 K, both the total rate coefficient k(1)(T,p) and the products are functions of pressure. For 700 K less than or equal to T less than or equal to 900 K, k(1)(T,p) is not always well defined in that the reactants can exhibit nonexponential decays in time. At sufficiently high pressure, the dominant product of the reaction changes from n-C4H5 to c-C4H5 (a four-numbered ring) to C4H4 + H, where C4H4 is vinyl acetylene, as the temperature is increased from 600 K to 900 K. For T > 900 K, the reaction can be written as an elementary step, C2H3 + C2H2 --> C4H4 + H (R1), With a rate coefficient, k(1) = 2.19 x 10(-12)T(0.163) exp(-8312/RT) cm(3)/(molecule.s), independent of pressure, even though the intermediate collision complex may suffer numerous collisions. We interpret our results in terms of the eigenvalues and eigenvectors of the G matrix, i.e., the relaxation/reaction matrix of the master equation. For T > 900 K, k(1)(T,p) always corresponds to the largest eigenvalue of G, which in turn corresponds to the zero-pressure-limit rate coefficient k(0)(T). The situation is more complicated at lower temperatures. Our predictions are in good agreement with the limited amount of experimental information available on the reaction. The quantum chemistry calculations indicate that both c-C4H5 and i-C4H5 are more stable than n-C4H5. The G2-like method gives results for the Delta H-f((0))(0 K) of c-C4H5 and i-C4H5 that are lower that that of n-C4H5 by 9.5 and 11.2 kcal/mol, respectively. The DFT-B3LYP results show similar differences of 6.0 and 13.7 kcal/mol, respectively.