Physical curiosity at the beginning, optical chaos is now attracting increasing interest in various technological areas such as detection and ranging or secure communications, to name but a few. However, the complexity of optical chaos generators still significantly hinders their development. In this context, the generation of chaotic polarization fluctuations in a single laser diode has proven to be a significant step forward, despite being observed solely for quantum-dot vertical-cavity surface-emitting lasers (VCSELs). Here, we demonstrate experimentally that a similar polarization dynamics can be consistently obtained in quantum-well VCSELs. Indeed, by introducing anisotropic strain in the laser cavity, we successfully triggered the desired chaotic dynamics. The simplicity of the proposed approach, based on low-cost and easily available components including off-the-shelf VCSELs, paves the way to the wide spread use of solitary VCSELs for chaos-based applications.