We use numerical simulations to demonstrate third-harmonic generation with near-unity nonlinear circular dichroism (CD) and high conversion efficiency ($ 10^{-2} text{W}^{-2}$) in asymmetric Si-on-SiO$_2$ metasurfaces. The working principle relies on the selective excitation of a quasi-bound state in the continuum, characterized by a very high ($>10^5$) quality-factor. By tuning multi-mode interference with the variation of the metasurface geometrical parameters, we show the possibility of independent control of linear CD and nonlinear CD. Our results pave the way for the development of all-dielectric metasurfaces for nonlinear chiro-optical devices with high conversion efficiency.