This paper deals with the optimal control of an obstacle problem where the control variable is the obstacle. The state system is described by a class of quasilinear elliptic variational inequalities with nonmonotone and nonsmooth perturbations. The cost functional is neither smooth nor convex, but locally Lipschitz continuous. The existence and approximation result of optimal solutions are proved. The optimality system is derived by Lagrange multiplier rules, smooth approximations, and nonsmooth analysis techniques.