  Consider the Kontsevich $\star$-product on the symmetric algebra of a finite
dimensional Lie algebra $\mathfrak g$, regarded as the algebra of distributions
with support 0 on $\mathfrak g$. In this paper, we extend this $\star$-product
to distributions satisfying an appropriate support condition. As a consequence,
we prove a long standing conjecture of Kashiwara-Vergne on the convolution of
germs of invariant distributions on the Lie group $G$.
