  Let M^3 be a closed CR 3-manifold. In this paper we derive a Bochner formula
for the Kohn Laplacian in which the pseudo-hermitian torsion plays no role. By
means of this formula we show that the non-zero eigenvalues of the Kohn
Laplacian are bounded below by a positive constant provided the CR Paneitz
operator is non-negative and the Webster curvature is positive. Our lower bound
for the non-zero eigenvalues is sharp and is attained on S^3. A consequence of
our lower bound is that all compact CR 3-manifolds with non-negative CR Paneitz
operator and positive CR Yamabe constant are embeddable. Non-negativity of the
CR Paneitz operator and positivity of the CR Yamabe constant are both CR
invariant conditions and do not depend on conformal changes of the contact
form. In addition we show that under the sufficient conditions above for
embeddability, the embedding is stable in the sense of Burns and Epstein. We
also show that for the Rossi example for non-embedability, the CR Paneitz
operator is negative. For CR structures close to the standard structure on
$S^3$ we show the CR Paneitz operator is positive on the space of pluriharmonic
functions with respect to the standard CR structure on $S^3$.
