  We study the dynamics of a ultra-cold boson gas in a lattice submitted to a
constant force. We track the route of the system towards chaos created by the
many-body-induced nonlinearity and show that relevant information can be
extracted from an experimentally accessible quantity, the gas mean position.
The threshold nonlinearity for the appearance of chaotic behavior is deduced
from KAM arguments and agrees with the value obtained by calculating the
associated Lyapunov exponent.
