Numerical simulations of freely propagating flames burning stoichiometric C $H_4$/CHC1$_3$/ $O_2$/$N_2$ mixtures are performed at atmospheric pressure in order to understand the effect of the $O_2$ enrichment level and the CHC1$_3$/C $H_4$ molar ratio. A chemical kinetic mechanism is developed, which involves 69 gas-phase species and 379 forward and 364 backward reactions. The calculated flame speeds are compared with the experiments for the flames established at several CHC1$_3$/C $H_4$ molar ratio (R<1), the results of which is in excellent agreement. As a results of the increased $O_2$ enrichment level from 0.21 to 1, the flame speed and the temperature in the burned gas are increased. At high CHC1$_3$/C $H_4$ molar ratio two peak values appear on the $O_2$ consumption rate, which are affected by CC1$_2$＋ $O_2$$_{-}$>C1O+CC1O and H＋ $O_2$$_{-}$>O＋OH.＋OH.