Chaotic foliations generalize Devaney's concept of chaos for dynamical systems. The property of a foliation to be chaotic is transversal, i.e, depends on the structure of the leaf space of the foliation. The transversal structure of a Cartan foliation is modeled on a Cartan manifold. The problem of investigating chaotic Cartan foliations is reduced to the corresponding problem for their holonomy pseudogroups of local automorphisms of transversal Cartan manifolds. For a Cartan foliation of a wide class, this problem is reduced to the corresponding problem for its global holonomy group, which is a countable discrete subgroup of the Lie automorphism group of an associated simply connected Cartan manifold. Several types of Cartan foliations that cannot be chaotic are indicated. Examples of chaotic Cartan foliations are constructed.