  A strictly convex real projective orbifold is equipped with a natural Finsler
metric called the Hilbert metric. In the case that the projective structure is
hyperbolic, the Hilbert metric and the hyperbolic metric coincide. We prove
that the marked Hilbert length spectrum determines the projective structure
only up to projective duality. A corollary is the existence of non-isometric
diffeomorphic strictly convex projective manifolds (and orbifolds) that are
isospectral. The corollary follows from work of Goldman and Choi, and Benoist.
