  We study the Chern-Simons action, which was defined for noncommutative spaces
in general by the author, for the noncommutative 3-torus, the universal
C*-algebra generated by 3 unitaries. D. Essouabri, B. Iochum, C. Levy, and A.
Sitarz constructed a spectral triple for the noncommutative 3-torus. We compute
the Chern-Simons action for this noncommutative space. In connection with this
computation we calculate the first coefficient in the loop expansion series of
the corresponding Feynman path integral with the Chern-Simons action as
Lagrangian. The result is independent of the deformation matrix of the
noncommutative 3-torus and always 0.
