  Using two-nucleon and three-nucleon interactions derived in the framework of
chiral perturbation theory (ChPT) with and without the explicit $\Delta$ isobar
contributions, we calculate the energy per particle of symmetric nuclear matter
and pure neutron matter in the framework of the microscopic
Brueckner-Hartree-Fock approach. In particular, we present for the first time
nuclear matter calculations using the new fully local in coordinate-space
two-nucleon interaction at the next-to-next-to-next-to-leading-order (N3LO) of
ChPT with $\Delta$ isobar intermediate states (N3LO$\Delta$) recently developed
by Piarulli et al. [arXiv:1606:06335]. We find that using this N3LO$\Delta$
potential, supplemented with a local N2LO three-nucleon interaction with
explicit $\Delta$ isobar degrees of freedom, it is possible to obtain a
satisfactory saturation point of symmetric nuclear matter. For this combination
of two- and three-nucleon interactions we also calculate the nuclear symmetry
energy and we compare our results with the empirical constraints on this
quantity obtained using the excitation energies to isobaric analog states in
nuclei and using experimental data on the neutron skin thickness of heavy
nuclei, finding a very good agreement with these empirical constraints in all
the considered nucleonic density range. In addition, we find that the explicit
inclusion of $\Delta$ isobars diminishes the strength of the three-nucleon
interactions needed the get a good saturation point of symmetric nuclear
matter. We also compare the results of our calculations with those obtained by
other research groups using chiral nuclear interactions with different
many-body methods, finding in many cases a very satisfactory agreement.
