We investigate the linear chain configurations of four-α clusters in 16O using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region of angular momentum (13-18ℏ) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia (ℏ2/2Θ∼0.06-0.08 MeV) can exist.