Dirac operator on the quantum sphere

We construct a Dirac operator on the quantum sphere S²_q which is covariant under the action of SU_q(2), compatible with a chirality operator, has the correct commutative limit and also a familiar fuzzy sphere limit. In the fuzzy sphere limit it reduces to Watamuras' Dirac operator. We argue that our Dirac operator may be useful in constructing SU_q(2) invariant field theories on S²_q following the Connes-Lott approach to noncommutative geometry.