  A widely accepted definition of ``quantum chaos'' is ``the behavior of a
quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics
of quantum-chaotic systems is nevertheless very different from that of their
classical counterparts. A fundamental reason for that is the linearity of
Schr{\"o}dinger equation. In this paper, we study the quantum dynamics of an
ultra-cold quantum degenerate gas in a tilted optical lattice and show that it
displays features very close to \emph{classical} chaos. We show that its phase
space is organized according to the Kolmogorov-Arnold-Moser theorem.
