Ampleness is a property that reflects the existence of geometric configurations behaving very much like projective space over a field. Pillay showed that the theory of the free group is 2-ample and conjectured that it not 3-ample. We show that the theory of the free group -and more generally the theory of any torsion-free hyperbolic group - is n-ample for any n. This is a joint work with Katrin Tent