chain model for the framed little discs operad naturally acts on the normalized Hochschild cochains of a unital associative algebra with a non–degenerate, symmetric, invariant bi–linear pairing. In fact, as in [@del], this operation can again be seen as a discretization of the calculations for the relations of a BV algebra up to homotopy on the chains of the operad $\Arc$ of [@KLP]. In [@cact] it is proven, that the operad of framed little discs is equivalent to the operad of cacti. Moreover, we gave a description of cacti in terms of a bi–crossed product of spineless cacti and an operad built on the monoid $S^1$ which we showed to be homotopy equivalent to the semi–direct product of these operads [@cact]. Furthermore, we gave a chain model for spineless cacti in terms of normalized spineless cacti which we showed to give a natural solution to Deligne’s conjecture [@del]. Using the description in terms of the bi–crossed and semi–direct products, we obtain a chain model for the operad of framed little discs, by tensoring the chains of normalized spineless cacti with the chains for the operad built on the monoid $S^1$. In order to prove the necessary relations on the chain 