The aim of the present numerical study was to illustrate the possible influence of translational nonequilibrium in the front of a shock wave on the rate of the threshold chemical reaction. The Monte Carlo method of nonstationary statistical simulation with variable weighting factors was used. Gas mixtures which contained, ahead of the front, two chemically interacting small additives $A_1$ , $A_2$ and an inert light main component were considered. A chemical reaction of the additives started in the front of a shock wave and led to formation of two new low-concentration components $A_3$ and $A_4$ . It was shown that for the ratio of molecular number densities of the additives $A_1$ , $A_2$ and an inert component $A_5$ of 1:10:200 and for the molecular mass ratio of components $A_1$ , $A_2$ , $A_3$ , $A_4$ , $A_5$ of 34.5:8:38.5:4:1 the value of the direct reaction rate obtained in the front exceeds its equilibrium value behind the wave by more than 100 times. As a result, the reaction occurs more intensively in the zone of translational nonequilibrium. It was also shown that for the cases of an exothermic reaction and a weak endothermic reaction, a small amount of the light reaction product has the velocity of the shock wave and is carried by the front.