This paper presents a method which is proposed to predict the design axial forces for zipper columns used in chevron steel bracing. This method is based on traditional capacity design principles and on examination of the seismic response of chevron bracing systems with zipper columns. It aims at maintaining the zipper column elastic under severe earthquake ground motions so that a complete plastic mechanism can develop in the structure, thereby preventing storey mechanisms resulting from a concentration of the inelastic demand along the building height. The design procedure was applied to a sample 8-storey frame and nonlinear time step dynamic analyses were performed to examine the frame response under ordinary and near-fault ground motions. The computed peak axial forces in the zipper column were found to vary with the ground motion type. They were well predicted by the proposed method, although the compression forces from the analyses were generally lower than those anticipated for the frame studied.