  Let A be a finite dimensional, unital, and associative algebra which is
endowed with a non-degenerate and invariant inner product. We give an explicit
description of an action of cyclic Sullivan chord diagrams on the normalized
Hochschild cochain complex of A. As a corollary, the Hochschild cohomology of A
becomes a Frobenius algebra which is endowed with a compatible BV operator. If
A is also commutative, then the discussion extends to an action of general
Sullivan chord diagrams. Some implications of this are discussed.
