For any cosmological constant Λ = −3/$l^2$ < 0 and any $\alpha$ < 9/4, we find a Kerr-AdS spacetime ($M$, $g_{KAdS}$), in which the Klein-Gordon equation $\square g_{KAdS}$ ψ+$\alpha$/$l^2$ψ = 0 has an exponentially growing ...