  We show that the radial MASA in the orthogonal free quantum group algebra
L(FO_N) is maximal amenable if N is large enough, using the Asymptotic
Orthogonality Property. This relies on a detailed study of the corresponding
bimodule, for which we construct in particular a quantum analogue of
R\u{a}dulescu's basis. As a byproduct we also obtain the value of the
Puk\'anszky invariant for this MASA.
