Tailless airplanes with swept wings rely on variations of the spanwise lift distribution to provide controllability in roll, pitch and yaw. Conventionally, this is achieved utilizing multiple control surfaces, such as elevons, on the wing trailing edge. As every flight condition requires different control moments (e.g. to provide pitching moment equilibrium), these surfaces are practically permanently displaced. Due to their nature, causing discontinuities, corners and gaps, they bear aerodynamic penalties, mostly in terms of shape drag. Shape adaptation, by means of chordwise morphing, has the potential of varying the lift of a wing section by deforming its profile in a way that minimizes the resulting drag. Furthermore, as the shape can be varied differently along the wingspan, the lift distribution can be tailored to each specific flight condition. For this reason, tailless aircraft appear as a prime choice to apply morphing techniques, as the attainable benefits are potentially significant. In this work, we present a methodology to determine the optimal planform, profile shape, and morphing structure for a tailless aircraft. The employed morphing concept is based on a distributed compliance structure, actuated by Macro Fiber Composite (MFC) piezoelectric elements. The multidisciplinary optimization is performed considering the static and dynamic aeroelastic behavior of the resulting structure. The goal is the maximization of the aerodynamic efficiency while guaranteeing the controllability of the plane, by means of morphing, in a set of flight conditions.