  We compute three-point correlation functions in the near-extremal,
near-horizon region of a Kerr black hole, and compare to the corresponding
finite-temperature conformal field theory correlators. For simplicity, we focus
on scalar fields dual to operators ${\cal O}_h$ whose conformal dimensions obey
$h_3=h_1+h_2$, which we name \emph{extremal} in analogy with the classic $AdS_5
\times S^5$ three-point function in the literature. For such extremal
correlators we find perfect agreement with the conformal field theory side,
provided that the coupling of the cubic interaction contains a vanishing
prefactor $\propto h_3-h_1-h_2$. In fact, the bulk three-point function
integral for such extremal correlators diverges as $1/(h_3-h_1-h_2)$. This
behavior is analogous to what was found in the context of extremal AdS/CFT
three-point correlators. As in AdS/CFT our correlation function can
nevertheless be computed via analytic continuation from the non-extremal case.
