In earthquake areas, an older chimney on the exterior wall of a home could be a hazard during an earthquake. If the chimney "falls" inward during an earthquake you might end up with all the chimney bricks on the floor of the room the fireplace is in. If the chimney falls outward it may damage a vehicle, the patio etc. Many chimneys on older homes in earthquake country are already damaged. An inspection by a professional will determine the exact condition of the chimney. In some cases in the past, damaged chimneys were converted to gas and an insert placed in the chimney.
If it is damaged, removing it might be a good solution. The exterior wall could then be closed up and a new "Zero Clearance" fireplace installed. This type of fireplace is much more efficient than the older variety (potential savings in heating costs) and it may be possible to vent it out the wall instead of thru the roof. Thus saying an area of potential water leak.
Come take a look at the website which I made for Home Sellers.