Let M denote a \(2n+1\) dimensional integrable CR manifold of hypersurface type with non-degenerate Levi form. In this paper, the author is interested in the problem of finding a pseudo-hermitian structure for which the Ricci tensor is a scalar multiple of the Levi form. The author terms such as a pseudo-Einstein structure. He shows that if M admits a closed, non-vanishing \((n+1,0))-\)form then M admits such a structure, and the existence of such a form is locally necessary for M to be pseudo- Einstein. It follows that M embeddeable in \({\mathbb{C}}^{n+1}\) implies M is pseudo-Einstein, and the author states some corollaries coming from known resuls about embeddability of CR manifolds. Further, the author presents a characterization of those functions which are locally the real part of CR functions on M. For example, in case \(n\geq 2\), the author shows U is CR pluriharmonic if and only if its covariant \((1-1)-\)Hessian is a pointwise scalar multiple of the Levi form. Another characterization is given in case \(\dim M=3.\) Finally the author relates the existence of a global pseudo-Einstein structure to the vanishing of the first Chern class of the holomorphic tangent bundle of M.