We examine the static and dynamic properties of polymer chains in a melt in the presence of a solid surface. A molecular dynamics simulation is carried out using a coarse-grained bead-spring model of polymer chains. Both attractive and repulsive interactions between surface and monomers are examined. Static conformations are characterized in terms of trains of attached monomers and detached loops and tails. We compare these conformations to a random walk model. Chain desorption rates are measured in order to calculate characteristic desorption times. We distinguish between chains which desorb rapidly after arriving at the surface and chains which reach a relaxed state at the surface and then desorb at a constant rate. A kinetic model is developed as a means to predict desorption rates and late time chain conformations.