We experimentally demonstrate enhanced third-harmonic generation from indium tin oxide nanolayers at telecommunication wavelengths with an efficiency that is approximately 600 times larger than crystalline silicon (Si). The increased optical nonlinearity of the fabricated nanolayers is driven by their epsilon-near-zero response, which can be tailored on-demand in the near-infrared region. The present material platform is obtained without any specialized nanofabrication process and is fully compatible with the standard Si-planar technology. The proposed approach can lead to largely scalable and highly integrated optical nonlinearities in Si-integrated devices for information processing and optical sensing applications.