The approximate analytical method is applied for analysis of the problem on local chain-thermal explosion in reaction of hydrogen oxidation in the presence of chemically active additive. It is shown that key parameters defining the critical size of a local source of ignition, are the temperature in the center of local ignition zone; quantity of the active centers of combustion created with the local source; and presence of active chemical additives in combustible gas mixture. Comparison to experimental data has shown applicability of the developed approach for the analysis of critical conditions of local ignition in combustible gas mixtures.