  We study the correlation functions of the integrable $O(n)$ spin chain in the
thermodynamic limit. We addressed the problem of solving functional equations
of the quantum Knizhnik Zamolodchikov type for density matrix related to the
$O(n)$ spin chain. We give the explicit solution for two-sites density matrix
elements for the $O(n)$ which are then evaluated for the $n=3,4,\dots,8$ cases
at zero temperature.
