A nonlocal density functional study of ethylene polymerization with a model for the heterogeneous Ziegler-Natta catalyst is presented. We have considered the propagation as well as the termination reactions. In the absence of a coordinated olefin. the Ti-C (chain) sigma bond does not occupy an octahedral coordination position but is oriented along an axis that is intermediate between the two octahedral coordination positions which are available. The propagation reaction occurs in a stepwise fashion, and the most favored mechanism requires a rearrangement of the growing chain out of the four-center transition-state plane. The insertion reaction is facilitated by a remarkable alpha-agostic interaction. The most favored termination reaction corresponds to the beta-hydrogen transfer to the monomer. This reaction is favored relative to the C-H sigma-bond activation of a coordinated monomer, as well as to the beta-hydrogen transfer to the metal.