Molecular dynamics simulations of realistic, united atom models of polyethylene undergoing uniaxial extension are described. Systems composed of chains ranging from 25 to 400 carbons have been studied, under a variety of processing histories, including isothermal deformation at constant applied stress below the melt temperature Tm, isothermal deformation below Tm followed by annealing, isothermal deformation above Tm followed by crystallization at a quench temperature below Tm, and non-isothermal crystallization during simultaneous deformation and cooling through Tm. Extension and orientation of large segments of flexible chains by uniaxial deformation accelerates the primary nucleation rate to a time scale accessible by molecular dynamics simulation. Entanglements operative during active deformation promote extension and orientation without nucleation of a crystal phase, while relaxation of stress at constant strain is sufficient to allow slippage of chains past pinning points and rapid nucleation and growth of crystallites as neighboring oriented chains come into registry. Isothermal crystallization of pre-oriented systems shows an apparent increase in nucleation density at lower temperatures; the resulting ordered regions are smaller and more closely aligned in the direction of orientation. During non-isothermal deformation, where stretching and cooling occur simultaneously, a first order transition is observed, with discontinuities in the volume and global order parameter, when the system crystallizes.