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The totally nonnegative Grassmannian $\mathrm{Gr}(k,n)_{\geq0}$ is the subsetof the real Grassmannian $\mathrm{Gr}(k,n)$ consisting of points with allnonnegative Pl\"ucker coordinates. The circular Bruhat order is a posetisomorphic to the face poset of A. Postnikov's (2005) positroid celldecomposition of $\mathrm{Gr}(k,n)_{\geq0}$. We provide a closed formula forthe sum of its weighted chains in the spirit of J. Stembridge (2002).

Counting weighted maximal chains in the circular Bruhat order