  In this paper, we prove uniqueness and nondegeneracy of positive solutions to
the following Kirchhoff equations with critical growth \begin{eqnarray*}
-\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u=u^{5}, & u>0 &
\text{in }\mathbb{R}^{3},\end{eqnarray*} where $a,b>0$ are positive constants.
This result has potential applications in singular perturbation problems
concerning Kirchhoff equaitons.
