  In this paper, we prove the large deviation estimates and Anderson
localization for CMV matrices on $\ell^2(\mathbb{Z}_+)$ with Verblunsky
coefficients defined dynamically by the hyperbolic toral automorphism. Part of
positivity results on the Lyapunov exponents of Chulaevsky-Spencer and Anderson
localization results of Bourgain-Schlag on Schr\"{o}dinger operators with
strongly mixing potentials are extended to CMV matrices.
