We study the effect of the nucleon-nucleon-lambda (NNΛ) three-body force on neutron stars. In particular, we consider the NNΛ force recently derived by the Jülich-Bonn-Munich group within the framework of chiral effective field theory at next-to-next-to-leading order. This force, together with realistic nucleon-nucleon, nucleon-nucleon-nucleon and nucleon-hyperon interactions, is used to calculate the equation of state and the structure of neutron stars within the many-body non-relativistic Brueckner-Hartree-Fock approach. Our results show that the inclusion of the NNΛ force leads to an equation of state stiff enough such that the resulting neutron star maximum mass is compatible with the largest currently measured (∼ 2 M ⊙ ) neutron star masses. Using a perturbative many-body approach we calculate also the separation energy of the Λ in some hypernuclei finding that the agreement with the experimental data improves for the heavier ones when the effect of the NNΛ force is taken into account.