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The Chern-Simons functional $S_{\rm CS}$ is an exact solution to theAshtekar-Hamilton-Jacobi equation of general relativity with a nonzerocosmological constant. In this paper we consider $S_{\rm CS}$ in Bianchi typeIX cosmology with $S^3$ spatial surfaces. We show that among the classicalsolutions generated by~$S_{\rm CS}$, there is a two-parameter family ofEuclidean spacetimes that have a regular NUT-type closing. When two of thethree scale factors are equal, these spacetimes reduce to a one-parameterfamily within the Euclidean Taub-NUT-de~Sitter metrics. For a nonzerocosmological constant, $\exp(iS_{\rm CS})$ therefore provides a semiclassicalestimate to the Bianchi~IX no-boundary wave function in Ashtekar's variables.Comment: 9 pages, REVTeX v3.0. (One reference added.

Chern-Simons functional and the no-boundary proposal in Bianchi type IX quantum cosmology