We use Monte Carlo simulations to estimate the rate of formation of a contact between the ends of a peptide chain as a function of its length N. We find that this rate decreases monotonically with N, in accord with the experimental data of Lapidus, Eaton, and Hofrichter [Proc. Natl. Acad. Sci. U.S.A. 97, 7220 (2000)] and of Bieri [Proc. Natl. Acad. Sci. U.S.A. 96, 9597 (1999)] but in contrast to previous theoretical work predicting a maximum of the rate for Nsimilar to10. By comparing our results with those data we estimate the diffusion coefficient for the relative diffusion of the chain ends to be Dsimilar to6x10(-6) cm(2)/s, which is close to that found for monomer diffusion.