The long time behaviour of a quantum chaotic system may be described using a random matrix theory, which for certain systems is dual to a 2D gravity model that allows for the creation and annihilation of baby universes.  In this talk I will present a field theory of closed topological strings, known as Kodaira-Spencer theory whose perturbative expansion reproduces the correlation functions of the matrix-theory and 2D gravity theory. To correctly describe the very long time behaviour of the correlation functions of the chaotic system  one needs to include non-perturbative effects, which in this approach are described in terms of a field theory of open topological strings, known as holomorphic Chern-Simons theory. By including a second non-perturbative saddle one reproduces the characteristic plateau behaviour of the chaotic correlators caused by the discreteness of the energy eigenvalues.