  We present the exact and explicit solution of the principal chiral field in
two dimensions for an infinitely large rank group manifold. The energy of the
ground state is explicitly found for the external Noether's fields of an
arbitrary magnitude. The exact Gell-Mann - Low function exhibits the asymptotic
freedom behaviour at large value of the field in agreement with perturbative
calculations. Coefficients of the perturbative expansion in the renormalized
charge are calculated. They grow factorially with the order showing the
presence of renormalons. At small field we found an inverse logarithmic
singularity in the ground state energy at the mass gap which indicates that at
$N=\infty$ the spectrum of the theory contains extended objects rather then
pointlike particles.
