  A class of exact rotating black hole solutions of gravity nonminimally
coupled to a self-interacting scalar field in arbitrary dimensions is
presented. These spacetimes are asymptotically locally anti-de Sitter manifolds
and have a Ricci-flat event horizon hiding a curvature singularity at the
origin. The scalar field is real and regular everywhere and its effective mass,
coming from the nonminimal coupling with the scalar curvature, saturates the
Breitenlohner-Freedman bound for the corresponding spacetime dimension. The
rotating black hole is obtained by applying an improper coordinate
transformation to the static one. Although both spacetimes are locally
equivalent, they are globally different, as it is confirmed by the nonvanishing
angular momentum of the rotating black hole. It is found that the mass is
bounded from below by the angular momentum in agreement with the existence of
an event horizon. The thermodynamical analysis is carried out in the grand
canonical ensemble. The first law is satisfied and a Smarr formula is
exhibited. The thermodynamical local stability of the rotating hairy black
holes is established from their Gibbs free energy. However, the global
stability analysis establishes that the vacuum spacetime is always preferred
over the hairy black hole. Thus, the hairy black hole is likely to decay into
the vacuum one for any temperature.
