The effects of polydispersity on the behavior of a polymer melt near a surface are investigated. The combined effects of the presence of a surface on the configurational freedom (entropy) of flexible chains and of the constraint that the total density is constant up to the surface yield a strikingly simple and general relation between the surface excess theta(N)(ex) and the bulk volume fraction phi(N)(b) of a component of chain length N in a polydisperse polymer melt: theta(N)(ex)/phi(N)(b) = A(1 - N/N-w), where A approximate to 0.195 is a numerical prefactor and N-w the weight-averaged chain length. This relation applies for any molecular weight distribution. Three different methods were used to obtain this law: (i) the numerical self-consistent field model of Scheutjens and Fleer, which is exact within a mean-field assumption, (ii) an analytical approximation of this model, which gives additional physical insight, and (iii) the analogy between the surface region of a polymer melt and an ideal polymer solution close to the adsorption/depletion transition.