The classical Harish-Chandra map, defined on a universal enveloping algebra of a semisimple Lie algebra g, identifies Casimir elements with polynomial invariants of a finite group (the Weyl group). An analogue of the Harish-Chandra map can be defined on a Clifford algebra of g. It turns out to identify primitive g-cocycles with an interesting orthogonal basis of the Cartan subalgebra of g.