This paper describes the design of an L1 adaptive Stability Augmentation System (SAS) for level 1 flying qualities, as defined in the Department of Defense Handbook for Flying Qualities of Piloted Aircraft, MIL-HDBK-1797. The SAS was developed for a Learjet 25 aircraft owned by Calspan Corporation for cruise and powered approach configurations. The structure of the flight control system consists of a baseline feedback controller, augmented with an L1 adaptive loop. This architecture supports two control objectives: i) the attainment, under nominal conditions, of the desired flying qualities with a simple control structure and a clear path for certification according to current regulations, and ii) the need for robust performance guarantees in the presence of severe off-nominal dynamics such as an engine failure, a shift in the center of mass, or reduced control effectiveness due to surface or hydraulic damage, to name a few examples. The baseline and adaptive portion of the flight control system were designed to be engaged and disengaged in flight independently, to evaluate the performance and robustness of each component separately. A preliminary evaluation of the flight control system is provided through simulation to conclude that: i) the baseline satisfies desired flying quality and robustness guidelines, but exhibits undesired behavior in the presence of severe off-nominal dynamics, and ii) the L1 adaptive augmentation does no harm in nominal conditions, provides robust performance in the presence of off-nominal dynamics, and a graceful degradation in the aircraft behavior as the severity of the off-nominal dynamics increases. A post-flight assessment of the flying and handling qualities of this flight control system can be found in the companion paper “Recovery of Desired Flying Characteristics with an L1 Adaptive Control Law: Flight Test Results on Calspan’s VSS Learjet”.