In this article we make theoretical predictions of the thermal rate coefficients for a series of elementary reactions on a C3H7 potential. Perhaps most importantly, we study the association/dissociation reactions for n-C3H7 and i-C3H7 [CH3 + C2H4(+M) reversible arrow n-C3H7(+M), C3H6 + H(+M) reversible arrow n-C3H7(+M), and C3H6 + H(+M) reversible arrow i-C3H7(+M)], where n-C3H7 and i-C3H7 are the propyl radicals and C3H6 is propene. However, in order to provide more information for our kinetic model, we have also included analyses of the association/elimination reaction [C3H6 + H reversible arrow CH3 + C2H4] and the abstraction reactions [C3H6 + H reversible arrow CH2CHCH2 + H-2, C3H6 + H reversible arrow CH3CCH2 + H-2, C3H6 + H reversible arrow CH3CHCH + H-2, and CH3 + C2H4 reversible arrow CH4 + C2H3]. The theory employs high-level electronic-structure methods to characterize the potential energy surface, conventional transition-state theory to calculate k(T) for the abstraction reactions, RRKM theory to calculate microcanonical, J-resolved rate coefficients for the dissociation processes, and master-equation methods to determine phenomenological rate coefficients k(T,p), for all of the nonabstraction reactions. The agreement between our theory and the experimental results available is remarkably good. The final results are cast in a form that is convenient for chemical kinetics modeling.