Block copolymers of $alpha$-methylstyrene with cyclohexyl methacrylate(CHMA) and methyl methacrylate(MMA) were successfully prepared by subsequent monomer addition technique via anionic living polymerization using s-BuLi as an initiator in the presence of LiCl in THF. It was found that the addition of LiCl to the polymerization system results in the narrowing of the molecular weight distribution (MWD) of the block copolymers-MWD value as low as 1.05. In the absence of LiCl, much broader MWD(larger than 1.1) was obtained due to the presence of deactivated poly($alpha$-methysltyrene) homopolymer. The polymerization behavior of CHMA was compared with that of MMA.