  We consider a model of one-dimensional Mott insulators coupled by a weak
interchain tunnelling $t_\perp$. We first determine the single-particle Green's
function of a single chain by exact field-theoretical methods and then take the
tunnelling into account by means of a Random Phase Approximation (RPA). In
order to embed this approximation into a well-defined expansion with a small
parameter, the Fourier transform $T_\perp(k)$ of the interchain coupling is
assumed to have a small support in momentum space such that every integration
over transverse wave vector yields a small factor $\kappa_0^2 \ll 1$. When
\tp(0) exceeds a critical value, a small Fermi surface develops in the form of
electron and hole pockets. We demonstrate that Luttinger's theorem holds both
in the insulating and in the metallic phases. We find that the quasi-particle
residue $Z$ increases very fast through the transition and quickly reaches a
value of about $0.4-0.6$. The metallic state close to the transition retains
many features of the one-dimensional system in the form of strong incoherent
continua.
