We propose a novel mechanism of cell motility, which relies on the coupling of actin polymerization at the cell membrane to geometric confinement. We consider a polymerizing viscoelastic cytoskeletal gel confined in a narrow channel, and show analytically that spontaneous motion occurs. Interestingly, this does not require specific adhesion with the channel walls, and yields velocities potentially larger than the polymerization velocity. The contractile activity of myosin motors is not necessary to trigger motility in this mechanism, but is shown quantitatively to increase the velocity. Our model qualitatively accounts for recent experiments which show that cells without specific adhesion proteins are motile only in confined environments while they are unable to move on a flat surface, and could help in understanding the mechanisms of cell migration in more complex confined geometries such as living tissues. ; Comment: 4 pages, 3 figures