For chains of regular injections of Hopf algebras the sets of maximal extended Jordanian twists {_k} are considered. We prove that under certain conditions there exists for ₀ the twist composed of the factors _{_k}. The general construction of a chain of twists is applied to the universal envelopings U( ) of classical Lie algebras . We study the chains for the infinite series A_n,B_n and D_n. The properties of the deformation produced by a chain U( ) are explicitly demonstrated for the case of = so(9).