In certain applications, such as the colocated control of flexible structures, the plant is known to be positive real. Hence, closed-loop stability is unconditionally guaranteed as long as the controller is also positive real. One approach to designing positive real controllers is the LQG-based positive real synthesis technique of Lozano-Leal and Joshi. The contribution of this paper is the extension of this positive real synthesis technique to include an H(infinity)-norm constraint on closed-loop performance.