Chimney Leaking and Carbon Monoxide

By nature of the word "leak", we must assume that we're speaking of a pressurized flue and the CO has magically "escaped", like a leaky water pipe. Even if the chimney has major cracks in the flue it is simply not possible for the CO to escape the flue unless the draft has been compromised. If the draft has been compromised, there are several things that can be happening, all of which are very dangerous:

the flue has a blockage
the flue has catastrophic failure, or a large breech to affect draft
there are adverse negative pressures in the building
there are no temperature differences for draft to take place
the chimney wasn't designed or installed properly
the heating appliance has been improperly installed or serviced, or simply neglected.

For these reasons, the trend has been moving towards sealed combustion appliances. These boilers and furnaces don't use a chimney; they vent out of a piping system that directly communicates to the outdoors without relying on natural draft, or what is commonly known as a chimney.

Again, if you have a carbon monoxide problem, the chimney is not the source of the problem, but it certainly could act as the delivery vehicle (not a trade phrase).