It is shown that optomechanical forces can cause nonlinear self-channeling of light in a planar dual-slab waveguide. A system of two parallel silica nanowebs, spaced similar to 100 nm and supported inside a fiber capillary, is studied theoretically and an iterative scheme developed to analyze its nonlinear optomechanical properties. Steady-state field distributions and mechanical deformation profiles are obtained, demonstrating that self-channeling is possible in realistic structures at launched powers as low as a few mW. The differential optical nonlinearity of the self-channeled mode can be as much as 10 x 10(6) times higher than the corresponding electronic Kerr nonlinearity. It is also intrinsically broadband, does not utilize resonant effects, can be viewed as a consequence of the extreme nonlocality of the mechanical response, and in fact is a notable example of a so-called accessible soliton.