  Using direct $N$-body simulations of self-gravitating systems we study the
dependence of dynamical chaos on the system size $N$. We find that the $N$-body
chaos quantified in terms of the largest Lyapunov exponent $\Lambda_{\rm max}$
decreases with $N$. The values of its inverse (the so-called Lyapunov time
$t_\lambda$) are found to be smaller than the two-body collisional relaxation
time but larger than the typical violent relaxation time, thus suggesting the
existence of another collective time scale connected to many-body chaos.
