The paper presents a design study for a morphing structural concept, which could be used to obtain a passively actuated high-lift wing configuration. A composite chiral honeycomb core is used to allow large variations of camber at limited strain levels in the structure of the aerodynamic surface. The design hypothesis is first assessed by means of structural analyses, which are performed applying two-dimensional and three-dimensional finite elements schemes. The results confirm the morphing capabilities in the chordwise direction of the structure, which still retains noteworthy axial and torsional stiffness properties. The aeroelastic performances of the morphing airfoil are then optimized, taking into account aeroelastic stability as well as strength constraints. The optimal parameters of chiral network and the required stiffness properties of the covering skin are identified. Overall, the work confirms the promising performances of morphing structures based on chiral topologies and assesses a numerical approach for the design of morphing aerodynamic structures