We study the behavior of a dilute solution of semiflexible polymer chains near a weakly attractive cylindrical surface using Monte Carlo simulation. The competition between monomer-monomer interactions and adsorption energy on the one hand, and bending energy and entropic penalty of adsorption on the other, leads to ordered conformations of the chains around the tube. Above a critical cylinder radius, the chains are found to be fully adsorbed in a monolayer. The preferred adsorbed conformations under such conditions are single and multiple helices. Our findings may shed light on the experimentally observed ordered polymer wrapping of carbon nanotubes. (c) 2007 Elsevier B.V. All rights reserved.