Chiral structures have many technologically significant applications in engineering. In this paper, we investigate, both theoretically and experimentally, the structural transformation from a symmetric X-shaped tensegrity to a chiral structure under uniaxial tension. When the applied tensile force exceeds a critical value, the initially achiral structure would exhibit snap-through buckling. At the critical state, the in-plane deformation mode of the tensegrity switches into an off-plane one. The critical condition of the structural transformation is provided in terms of structural parameters. An experiment was performed to validate the theoretical model. This work may not only deepen our understanding of the stability of tensegrities but also help design chiral structures for engineering applications.