  In this article we provide the Henon-Heiles system defined on
Lie-algebraically deformed nonrelativistic space-time with the commutator of
two spatial directions proportional to time. Particularly, we demonstrate that
in such a model the total energy is not conserved and for this reason the role
of control parameter is taken by the initial energy value $E_{0,{\rm tot}} =
E_{{\rm tot}}(t=0)$. Besides, we show that in contrast with the commutative
case, for chosen values of deformation parameter $\kappa$, there appears chaos
in the system for initial total energies $E_{0,{\rm tot}}$ below the threshold
$E_{0,{\rm th}} = 1/6$.
