This paper considers the problem of output feedback stabilization of unstable linear time-delay systems. The major features of the approach are: (1) the delay system is characterized by a fixed transfer function matrix that contains just the set of unstable or marginally unstable modes, plus an H-infinity-norm for the stable part, (2) the controller design is accomplished by dynamic output feedback, and (3) sufficient conditions in the form of two algebraic Riccati equations and an upper bound explicitly characterize a stabilizing controller. The method is restricted to delay systems that satisfy an upper bound on the stable part.