We shall review the evidence for the presence of a hidden hyperbolic Kac-Moody symmetry in the chaotic dynamics of cosmological singularities discovered by  Belinsky, Khalatnikov and Lifshitz. This hidden symmetry was first noticed in the dynamics of bosonic fields, but, remarkably, it  is also present in the dynamics of fermionic fields. Terms quartic in the gravitino of supergravity might lead to an avoidance of the zero-volume singularity, i.e. to a cosmological bounce.