Molecular dynamics simulations are performed to investigate the stable morphologies of semi-flexible polymer chains within a single wall carbon nanotube (CNT). We characterize these morphologies with a variety of measures. Due to the different curvature inside the CNT to outside, there are increased numbers of polymer-CNT bead contacts for polymers which reside inside the CNT. A sufficiently long polymer chain first adsorbs on the exterior of the nanotube and subsequently moves inside the cavity of the nanotube. At equilibrium, the polymer configuration consists of a central stem surrounded by helically wrapped layers. Sections of the polymer outside the CNT have helical conformations (for CNTs of small radius) or circular arrangements (for CNTs of larger radius). Polymers encapsulated within the CNT have an increased chirality due to packing of the beads and this chirality is further enhanced for moderately stiff chains.