The chain scattering approach to the solution of the linear time-invariant (LTI) H-infinity control problem proposed in Kimura (1995) is extended to the linear time-varying (LTV) case in this paper. A proof of sufficiency and necessity for (J(mr), J(pr))-lossless and co-(J(mq), J(mr))-lossless factorizations for the solvability of the four-block LTV H-infinity control problem is shown. The solutions obtained exist in the form of Lyapunov stabilizing solutions to two matrix Riccati differential equations and satisfy a spectral radius coupling condition. A state space proof is also given for the LTV co-(J(mq), J(mr))-lossless embedding theorem in H-infinity by exploiting the cascade structure of the dual chain scattering formalism and the structural decomposition of the system.