If it doesn't burn the house down....it will probably wreck your chimney and scare you half to death. Here's how it happens:
Start with one dirty chimney-- let's say a fireplace that hasn't been cleaned for a couple of years. The soot lining the interior of the chimney flue is saturated with a flammable material called creosote. (More detail on creosote is available with a simple google search on the topic) It doesn't take much to ignite creosote -- a newspaper fire sending flames up to the damper can sometimes be enough to set off a major fire.
How To Control a Chimney Fire
A chimney fire can be controlled with quick action and proper techniques. If possible, put the fire out with an extinguisher or sand. Cover the opening with a wet blanket and then call the fire department immediately. A reasonable alternative to all of this is having your chimney inspected and cleaned on a regular basis. Call for more information and we'll be glad to answer any questions you have may about the cost or process.