We consider a Hamiltonian particle system interacting by means of a pair potential. We look at the behavior of the system on a space scale of order e^(-1), times of order e^(-2) and mean velocities of order e, with e a scale parameter. Assuming that the phase space density of the particles is given by a series in e (the analog of the Chapman-Enskog expansion), the behavior of the system under this rescaling is described, to the lowest order in e, by the incompressible Navier-Stokes equations. The viscosity is given in terms of microscopic correlations, and its expression agrees with the Green-Kubo formula.