We present the results of a series of molecular dynamics simulations of a melt of flexible bead-spring polymer chains with a single static cylindrical inclusion with diameter equal to the polymer beads. Chains of length N = 10, 25, 50, 100 and polymer/inclusion interactions, which are attractive with well depths of 1, 4, and 10 epsilon, and athermal, are considered. We show that the distribution in winding number of a polymer chain about the inclusion may be approximated by Belisle's probability distribution for the winding of a random walk about a point. The degree of winding per chain increases as the polymer/inclusion attraction increases because of the larger number of monomers pulled into runs of sequential monomers at the inclusion. Runs accumulate more winding than do loops or tails, and the amount of winding a given run accumulates increases with increasing polymer/inclusion attraction due to increased likelihood of perpendicular bond orientation with respect to the inclusion. The probability of winding depends on monomer distance from the inclusion in an apparently universal manner when distance is scaled by the unperturbed chain radius of gyration. Our results bear direct relevance to understanding the nature of enhancing toughness of polymeric materials by adding filler particles which increase the degree of entanglement.