Nobody knows for sure the answer to this question. The fire began in or near a barn on DeKoven St. belonging to Mrs. Catherine O'Leary.
There is a colorful legend that persists to this day, that the fire was started by a cow, belonging to Mrs. O'Leary, kicking over a lantern. While Mrs. O'Leary, and presumably her cow as well, were real, the story was published because it simply made a good story. This is one of many examples of the Yellow Journalism of the period, and apparently, Mrs. O'Leary spent the rest of her days unhappily in the public eye, blamed for the huge fire until the end of her life.