  We compute the running QCD coupling on the lattice by evaluating two-point
and three-point off-shell gluon Green's functions in a fixed gauge and imposing
non-perturbative renormalisation conditions on them. Our exploratory study is
performed in the quenched approximation at beta=6.0 on 16^4 and 24^4 lattices.
We show that, for momenta in the range 1.8-2.3 Gev, our coupling runs according
to the two-loop asymptotic formula, allowing a precise determination of the
corresponding Lambda parameter. The role of lattice artifacts and finite-volume
effects is carefully analysed and these appear to be under control in the
momentum range of interest. Our renormalisation procedure corresponds to a
momentum subtraction scheme in continuum field theory, and therefore lattice
perturbation theory is not needed in order to match our results to the MSbar
scheme, thus eliminating a major source of uncertainty in the determination of
alpha_MSbar. Our method can be applied directly to the unquenched case.
