This article deals with distributed parameter systems described by first-order hyperbolic partial differential equations (PDEs), for which the manipulated input, the controlled output, and the measured output are distributed in space. For these systems, a general output-feedback control methodology is developed employing a combination of theory of PDEs and concepts from geometric control. A concept of characteristic index is introduced and used for the synthesis of distributed state-feedback laws that guarantee output tracking in the closed-loop system. Analytical formulas of distributed output-feedback controllers are derived through combination of appropriate distributed state observers with the developed state-feedback controllers. Theoretical analogies between our approach and available results on stabilization of linear hyperbolic PDEs are also identified. The developed control methodology is implemented on a nonisothermal plug-flow reactor and its performance is evaluated through simulations.