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We study a one-dimensional model of interacting conduction electrons with atwo-fold degenerate band away from half filling. The interaction includes anon-site Coulomb repulsion and Hund's rule coupling. We show that suchone-dimensional system has a divergent Cooper pair susceptibility at T = 0,provided the Coulomb interaction $U$ between electrons on the same orbital andthe modulus of the Hund's exchange integral $|J|$ are larger than theinterorbital Coulomb interaction. It is remarkable that the superconductivitycan be achieved for {\it any} sign of $J$. The opening of spectral gaps makesthis state stable with respect to direct electron hopping between the orbitals.The scaling dimension of the superconducting order parameter is found to bebetween 1/4 (small $U$) and 1/2 (large $U$).Comment: 11 pages, Latex, no figure

Superconductivity in a spin liquid: A one-dimensional example