Looks like burning

so if fire it just extremely rapid exothermic oxidation, maintained as a chain reaction by the abundance of oxygen in the atmosphere, wouldn't that mean that any chemical reaction that required some heat to trigger, and which produced enough heat to maintain itself, in the presence of whatever chemicals we're talking about in a free and usable form, would create a fire-like thing without requiring oxygen?
I don't know enough chemistry, here, but fire's a favorite subject of mine, so if anyone can fill me in, please do. Can there be anaerobic fire?