An analogue of a spectral triple over SUq(2) is constructed for which the usual assumption
of bounded commutators with the Dirac operator fails. An analytic expression analogous to that
for the Hochschild class of the Chern character for spectral triples yields a non-trivial twisted
Hochschild 3-cocycle. The problems arising from the unbounded commutators are overcome by
defining a residue functional using projections to cut down the Hilbert space.