We calculate static properties of non-rotating neutron stars (NS's) using a microscopic equation of state (EOS) for asymmetric nuclear matter, derived from the Brueckner-Bethe-Goldstone many-body theory with explicit three-body forces. We use the Argonne AV14 and the Paris two-body nuclear force, implemented by the Urbana model for the three-body force. We obtain a maximum mass configuration with Mmax = 1.8 M_☉ (Mmax = 1.94 M_☉) when the AV14 (Paris) interaction is used. They are both consistent with the observed range of NS masses. The onset of direct Urca processes occurs at densities n >= 0.65 fm(-3) for the AV14 potential and n >= 0.54 fm(-3) for the Paris potential. Therefore, NS's with masses above M(Urca) = 1.4 M_☉ for the AV14 and M(Urca) = 1.24 M_☉ for the Paris potential can undergo very rapid cooling, depending on the strength of superfluidity in the interior of the NS. The comparison with other microscopic models for the EOS shows noticeable differences.