  Let $(S,L)$ be a Lie-Rinehart pair such that $L$ is $S$-projective and let
$U$ be its universal enveloping algebra. The purpose of this paper is to
present a spectral sequence which converges to the Hochschild cohomology of $U$
and whose second page involves the Lie-Rinehart cohomology of the pair and the
Hochschild cohomology of $S$ with values on $U$.
