No, a cow probably did not cause the Chicago fire in 1871, although the fire did start in the O’Leary’s barn.
There’s no reason to believe the fire was anything more than the result of an extraordinary dry spell of weather mixed with the practice of keeping dry wood chips around as a cheap source of fuel.
A cigarette, a match, an ember from a burning stove nearby, or even spontaneous combustion would have been more than enough to set the blaze going. Incidentally, a much bigger, more deadly fire happened on the exact same night in Peshtigo, Wisconsin.
It was started by railroad workers clearing a way for new tracks. As a result of the dry air, a small brush fire turned into a blazing inferno.
Before the fire went out almost a week later it had burned over 1.2 million acres and caused more than $169 million dollars worth of damage—about the same dollar amount of the property lost in the Chicago blaze.
On top of that, over 1,200 people were killed by the Wisconsin fire—four times as many as the Chicago fire. It didn’t get as much publicity, though.