The mid-wave infrared (MWIR) spectral region (3-5 {mu}m) is important to a vast variety of applications in imaging, sensing, spectroscopy, surgery, and optical communications. Efficient third-harmonic generation (THG), converting light from the MWIR range into the near-infrared, a region with mature optical detection and manipulation technologies, offers the opportunity to mitigate a commonly recognized limitation of current MWIR systems. In this work, we present the possibility of boosting THG in the MWIR through a metasurface design. Specifically, we demonstrate a 30-fold enhancement in a highly nonlinear phase change material Ge2Sb2Se4Te1 (GSST), by patterning arrays of subwavelength cylinders supporting a magnetic dipolar resonance. The unprecedented broadband transparency, large refractive index, and remarkably high nonlinear response, together with unique phase-change properties, make GSST-based metasurfaces an appealing solution for reconfigurable and ultra-compact nonlinear devices operating in the MWIR.