We calculate the nuclear energy density functional relevant for N = Z even-even nuclei in the framework of chiral perturbation theory. The calculation includes the one-pion exchange Fock diagram and the iterated one-pion exchange Hartree and Fock diagrams. From these few leading order contributions in the small momentum expansion one obtains already a good equation of state of isospin symmetric nuclear matter. We find that in the region below the nuclear matter saturation density the effective nucleon mass M * (ρ) deviates by at most 15% from its free space value M, with 0.89M < M * (ρ) < M for ρ < 0.11 fm -3 and M * (ρ) > M for higher densities. The parameterfree strength of the ( ∇ρ) 2 -term, F ∇ (k f ), is at saturation density comparable to that of phenomenological Skyrme forces. The magnitude of F J (k f ) accompanying the squared spin-orbit density J 2 comes out considerably larger. The strength of the nuclear spin-orbit interaction, F so (k f ), as given by iterated one-pion exchange is about half as large as the corresponding empirical value, however, with the wrong negative sign. The novel density dependencies of M * (ρ) and F ∇,so,J (k f ) as predicted by our parameterfree (leading order) calculation should be examined in nuclear structure calculations (introducing at least an additional short range spin-orbit contribution constant in density).