  Let $G$ be a finite group or a compact connected Lie group and let $BG$ be
its classifying space. Let $\mathcal{L}BG:=map(S^1,BG)$ be the free loop space
of $BG$ i.e. the space of continuous maps from the circle $S^1$ to $BG$. The
purpose of this paper is to study the singular homology $H_*(\mathcal LBG)$ of
this loop space. We prove that when taken with coefficients in a field the
homology of $\mathcal LBG$ is a homological conformal field theory. As a
byproduct of our main theorem, we get a Batalin-Vilkovisky algebra structure on
the cohomology $H^*(\mathcal LBG)$. We also prove an algebraic version of this
result by showing that the Hochschild cohomology $HH^*(S_* (G),S_*(G))$ of the
singular chains of $G$ is a Batalin-Vilkovisky algebra.
