Abstract: An incinerator having a first combustion chamber capable of receiving material to be incinerated, a second combustion chamber capable of receiving the flue gas, and a particulate extraction and containment system connecting the two is provided. Also provided is a method for incineration which involves combusting a material using a substoichiometric amount of oxygen so as to produce a flue gas, collecting the flue gas, cooling the flue gas, and combusting the flue gas using at least a stoichiometric amount of oxygen. The incinerator and method allow for the removal of toxins and toxin precursors prior to exposure to stoichiometric or greater levels of oxygen and to temperatures greater than 1000.degree. F. Moreover, the incinerator and method provide for the recycling of materials and a reduction of waste volume to a level below that which is currently obtainable.