  A recent calculation of the nuclear energy density functional from chiral
two- and three-nucleon forces is extended to the isovector terms pertaining to
different proton and neutron densities. An improved density-matrix expansion is
adapted to the situation of small isospin-asymmetries and used to calculate in
the Hartree-Fock approximation the density-dependent strength functions
associated with the isovector terms. The two-body interaction comprises of
long-range multi-pion exchange contributions and a set of contact terms
contributing up to fourth power in momenta. In addition, the leading order
chiral three-nucleon interaction is employed with its parameters fixed in
computations of nuclear few-body systems. With this input one finds for the
asymmetry energy of nuclear matter the value $A(\rho_0) \simeq 26.5\,$MeV,
compatible with existing semi-empirical determinations. The strength functions
of the isovector surface and spin-orbit coupling terms come out much smaller
than those of the analogous isoscalar coupling terms and in the relevant
density range one finds agreement with phenomenological Skyrme forces. The
specific isospin- and density-dependences arising from the chiral two- and
three-nucleon interactions can be explored and tested in neutron-rich systems.
