  We study correlations of observables in energy eigenstates of chaotic systems
of a large size $N$. We show that the bipartite entanglement of two subsystems
is quite strong, whereas macroscopic entanglement of the total system is
absent. It is also found that correlations, either quantum or classical, among
less than $N/2$ points are quite small. These results imply that chaotic states
are stable. Invariance of these properties under local operations is also
shown.
