Within the one-loop approximation of baryon chiral perturbation theory we calculate all one-pion and two-pion exchange contributions to the nucleon-nucleon interaction. In fact we construct the elastic NN-scattering amplitude up to and including third order in small momenta. The phase shifts with orbital angular momentum L ≥2 and the mixing angles with J ≥ 2 are given parameter free and thus allow for a detailed test of chiral symmetry in the two-nucleon system. We find that for the D-waves the 2π-exchange corrections are too large as compared with empirical phase shifts, signaling the increasing importance of shorter range effects in lower partial waves. For higher partial waves, especially for G-waves, the model-independent 2π-exchange corrections bring the chiral prediction close to empirical NN phase shifts. We propose to use the chiral NN phase shifts with L ≥ 3 as input in a future phase-shift analysis. Furthermore, we compute the irreducible two-pion exchange NN potentials in coordinate space. They turn out to be of van der Waals type, with exponential screening of two-pion mass range.