  We calculate the nuclear energy density functional relevant for N=Z even-even
nuclei in the systematic 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 very good
equation of state of isospin symmetric nuclear matter. We find that in the
region below nuclear matter saturation density the effective nucleon mass
$\widetilde M^*(\rho)$ deviates by at most 15% from its free space value $M$,
with $0.89M<\widetilde M^*(\rho)<M$ for $\rho < 0.11 {\rm fm}^{-3}$ and
$\widetilde M^*(\rho)>M$ for higher densities. The parameterfree strength of
the $(\vec\nabla \rho)^2$-term, $F_\nabla(k_f)$, is at saturation density
comparable to that of phenomenological Skyrme forces. The magnitude of
$F_J(k_f)$ accompanying the squared spin-orbit density $\vec J ^2$ comes out
somewhat 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 $\widetilde M^*(\rho)$ and $F_{\nabla,so,J}(k_f)$
as predicted by our parameterfree calculation should be examined in nuclear
structure calculations (after introducing an additional short range spin-orbit
contribution constant in density).
