A three-dimensional structural topology optimization framework is applied to the problem of aircraft wing design. The approach presented is unique in that the working domain of the design problem is given by the full three-dimensional region inside the wing skin, with no assumptions being made with regard to the number, location or orientation of the structural members. The wing is modelled as an elongated cantilever beam with a taper ratio of 0.7 in both chord and thickness. Distributed, pressure-type loading is applied to the top and bottom surfaces. The optimization is performed using a level set method, with advection velocities given by classical shape sensitivity information along the material boundary. We also devise a method for enforcing local stress constraints that accounts for the void regions associated with topology optimization problems and is consistent with the level set approach used.