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We consider the $\theta$-deformed quantum three sphere $S^3_\theta$ and studyits Chern--Simons theory from a spectral point of view. We first construct aspectral triple on $S^3_\theta$ as a generalization of the Dirac geometry on$S^3 $. Since the choice of Dirac operator is not unique, we give two morenatural spectral triples on $S^3_\theta$ related to the standard round metric.We then compute the Chern--Simons action with respect to the three spectraltriples, it turns out that it is not a topological invariant, that is, itdepends on the choice of Dirac operators.

Noncommutative Chern-Simons theory on the quantum 3-sphere $S^3_\theta$