We extende the resolution of the Yamabe conjecture to the Cauchy-Riemann manifolds and precisely the case left open by D. Jenson and J. Lee: the conformally flat case and the case n = 1, where 2n + 1 is the dimension of the CR manifold. Let (M, ϑ) be a compact CR manifold of dimension 2n + 1 and ϑ a contact form. The CR Yamabe conjecture states that there is a contact form ϑ on M, conformal to ϑ, which has a constant Webster curvature. The problem is equivalent to the existence of a strictly positive solution of the equation LMu = u^1+2/n