In this paper, we consider the simultaneous H-infinity stabilization problem of l plants via the chain scattering framework. By exploiting the free parameter in the parameterization of stabilizing H-infinity controllers, we will show that the solvability of the simultaneous H-infinity stabilization problem of l-plants is equivalent to the simultaneous strongly H-infinity stabilization of an associated l - 1 systems by a single strongly stabilizing H-infinity controller. It will be demonstrated that the cascading structure of the chain scattering framework makes it easy to formulate the problem and the resulting solution with clarity. We will also present a sufficient condition in the form of solutions to two algebraic Riccati equations (AREs) to solve the strongly H-infinity stabilization problem. Numerical examples are given to illustrate our approach.