We present a non-supersymmetric theory with non-vanishing 4D curvature with a naturally light dilaton. It is based on a 5D holographic description of a conformal theory perturbed by a close-to-marginal operator of dimension 4-epsilon, which develops a condensate. As long as the dimension of the perturbing operator remains very close to marginal in the IR, and there is no large contribution to the 4D curvature from UV physics, a stable minimum at hierarchically small scales is achieved, where the dilaton mass squared is suppressed by epsilon. At the same time the cosmological constant in this sector is also suppressed by epsilon.