  We study limiting distribution of pair counting statistics of the form $
\sum_{1\leq i\neq j\leq N} f(L_N\*(\theta_i-\theta_j))$ for the circular
$\beta$-ensemble (C$\beta$E) of random matrices for sufficiently smooth test
function $f$ and $L_N=O(N).$ For $\beta=2$ and $L_N=N$ our results are inspired
by a classical result of Montgomery on pair correlation of zeros of Riemann
zeta function.
