  The method of unitary transformations generates five classes of leading-order
reducible chiral four-nucleon interactions which involve pion-exchanges and a
spin-spin contact-term. Their first-order contributions to the energy per
particle of isospin-symmetric nuclear matter and pure neutron matter are
evaluated in detail. For most of the closed four-loop diagrams the occurring
integrals over four Fermi-spheres can be reduced to easily manageable one- or
two-parameter integrals. One observes substantial cancelations among the
different contributions arising from 2-ring and 1-ring diagrams. Altogether,
the net attraction generated by the chiral four-nucleon interaction does not
exceed values of $-1.3$\,MeV for densities $\rho<2\rho_0$.

Nuclear Theory