  Let $X$ be a simply connected space and $\Bbb K$ be any field. The normalized
singular cochains $N^*(X; {\Bbb K})$ admit a natural strongly homotopy
commutative algebra structure, which induces a natural product on the
Hochschild homology $HH_* N^*X$ of the space $X$. We prove that, endowed with
this product, $HH_*N^*X$ is isomorphic to the cohomology algebra of the free
loop space of $X$ with coefficients in $\Bbb K$. We also show how to construct
a simpler Hochschild complex which allows direct computation.
