Dirac operator on the quantum sphere

We construct a Dirac operator on the quantum sphere S2q which is covariant under the action of SUq(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 Watamurasʹ Dirac operator. We argue that our Dirac operator may be useful in constructing SUq(2) invariant field theories on S2q following the Connes–Lott approach to noncommutative geometry.