Chiral photonics enables the control of light handedness for many applications in optical communications, biological and chemical sensing, and quantum technologies. While traditional approaches focus on engineering strong linear chiroptical response, nonlinear chiral phenomena remain largely unexplored. Here, we demonstrate experimentally a pronounced nonlinear chiral response of free-standing membrane metasurfaces that are effectively achiral in the linear regime. By employing patterned silicon membranes with both C4 symmetry and intentionally broken in-plane symmetry, we reveal that strong nonlinear circular dichroism can be observed in the third-harmonic generation. An unperturbed metasurface exhibits a strong cross-polarized third-harmonic signal with nonlinear circular dichroism of the value -0.83, whereas in-plane symmetry breaking enables a copolarized channel, and it reverses the sign of the nonlinear circular dichroism, reaching values as large as 0.41. Our findings suggest a novel approach for engineering nonlinear chiral responses in metasurfaces, complementing traditional approaches and paving the way toward advanced chiral metadevices.