  We study the largest Lyapunov exponent $\lambda$ and the finite size effects
of a system of N fully-coupled classical particles, which shows a second order
phase transition. Slightly below the critical energy density $U_c$, $\lambda$
shows a peak which persists for very large N-values (N=20000). We show, both
numerically and analytically, that chaoticity is strongly related to kinetic
energy fluctuations. In the limit of small energy, $\lambda$ goes to zero with
a N-independent power law: $\lambda \sim \sqrt{U}$. In the continuum limit the
system is integrable in the whole high temperature phase. More precisely, the
behavior $\lambda \sim N^{-1/3}$ is found numerically for $U > U_c$ and
justified on the basis of a random matrix approximation.
