This paper investigates the decay properties of solutions to the massive
linear wave equation $\Box_g \psi + \frac{{\alpha}}{l^2} \psi =0$ for $g$ the
metric of a Kerr-AdS spacetime satisfying $|a|l<r_+^2$ and $\alpha<9/4$
satisfying the Breitenlohner Freedman bound. We prove that the non-degenerate
energy of $\psi$ with respect to an appropriate foliation of spacelike slices
decays like $(\log t^\star)^{-2}$. Our estimates are expected to be sharp from
heuristic and numerical arguments in the physics literature suggesting that
general solutions will only decay logarithmically. The underlying reason for
the slow decay rate can be traced back to a stable trapping phenomenon for
asymptotically anti de Sitter black holes which is in turn a consequence of the
reflecting boundary conditions for $\psi$ at null-infinity.