Molecular dynamics simulations of ethylene polymerization have been performed using a chemically realistic, reactive potential. These simulations have been performed in the bulk liquid and in the interior of both (10,10) and (7,7) nanotubes as a means of investigating the effects of nanoscale confinement on the polymerization reaction. The structure of the resulting polymer was found to be similar in the bulk and in the (10,10) tube at the elevated temperatures investigated, while only very small oligomers were formed in the (7,7) tube. The reaction rate was substantially reduced in the nanotubes, when compared to the bulk, primarily as a result of spatial interference due to reaction products. These simulations have implications for the possible use of nanotubes as synthetic reaction vessels, as well as for the general understanding of association reactions in confined spaces.