We adopt two- and three-body nuclear forces derived at the next-to-next-to-leading-order in the framework of effective chiral perturbation theory to calculate the equation of state of β-stable neutron star matter using the Brueckner–Hartree–Fock many-body approach. We use the recent optimized chiral two-body nuclear interaction at next-to-next-to-leading-order derived by Ekström et al. and two different parametrizations of the three-body next-to-next-to-leading-order interaction: the first one is fixed to reproduce the saturation point of symmetric nuclear matter while the second one is fixed to reproduce the binding energies of light atomic nuclei. We show that in the second case the properties of nuclear matter are not well determined whereas in the first case various empirical nuclear matter properties around the saturation density are well reproduced. We finally calculate various neutron star properties and in particular the mass-radius and mass-central density relations. We find that the adopted interactions based on a fully microscopic framework, are able to provide an equation of state which is consistent with the present data of measured neutron star masses.