Perhaps you will get a pleasant surprise on Friday when the mason provides an estimate. $3k seems awfully high. Usually a chimney rebuild means from the roof line up; that's where years of exposure to the weather causes problems. These problems, however, are nearly always due to deterioration of the mortar, not the bricks (assuming that's what you have)themselves. Sometimes repointing the bricks is all that is needed; other times the chimney is dismantled to just below the roof line,and the bricks are cleaned and reused. In either case, a relatively small portion of the chimney is involved. It would be very, very unusual for a chimney to have suffered damage inside the house. A steep roof with a high chimney necessitating a good deal of scaffolding would, of course, increase labor costs a good deal. If they are available in your area, there are systems for lining and strenghthening chimneys with a poured in place liner. Supaflu (www.supaflu.com) is one such system with which I have been personally very satisfied. A safe, usable chimney is a very real asset in any house. It may be cheaper in the short term to simply abandon the chimney, but I would guess you'll be losing a good deal more than $3k in resale value by doing so.

The third picture seems to show the shingling job directing water right to the base of the chimney chase (the wooden chimney enclosure.) There's no sign of any flashing in the picture, but there may be some. In any case, something must be done to divert water away from this area. Any sort of repair would be short lived with water continuing to pour into this intersection between roof and chase. Never should have been roofed this way in the first place.

So the zero-clearance fireplaces are actually in all technical terms, wood stoves, that are designed to be in close proximity to flammable objects (ie. walls), which allows them to be inserted into a chimney cove much like a fireplace. But in reality, the design in such that they have a fresh-air intake that draws cool air from outside, feeds through the fire, often INCLUDING a catalytic converter if you have a high efficiency one (which most do now of days), which re-burns to reduce creosote build-up and then expels the smoke and soot up a stove-pipe just like what is used for wood stoves...only they're usually not as visually attractive because they are tucked inside a false "chimney" chase. There are some reasons why soot builds up on the exterior of your chimney, and some things you should consider that could be causes: 1) As Renovator says, down-draft can cause excessive soot build-up, along with starved cool fires. You need to consider if you burn your fire nice and hot (blue flames) or if you tend to have cool burns (which are often "showier" fires). This also applies for the insulation of your chimney. If you are in a cold climate, it is usually recommended that unless you have a catalytic converter (and even then really), to insulate your chase to the TOP, right to the point of the chimney pan. This keeps the chimney pipe warm all the way to the top, reducing the cold down-draft and the settling of soot within your chimney pipe. It is possible that your chimney chase is not insulated the entire length, and that it is cooling in the last couple of feet, causing the creosote to settle out shortly after it leaves the chimney. 2) What type of wood do you burn? Different wood has different levels of creosote that they release. Are you burning sappy woods? Are you burning woods like poplar that break down very quickly in fires, meaning you're burning twice as much fuel? 3) Is your wood dry? This is a HUGE one, as wet wood increases your creosote. Just because it's dry to touch, does not mean it's dry wood. What are your storage conditions? What is the humidity where it is kept? Does it acclimate in your home before burning? How long ago was it cut? Is there any rotting that could retain excess moisture? 4) How high above the top of your chimney pan is your chimney cap? Most designers will extend the chimney pipe 1 to 2' above the chimney pan, so that the soot will travel away from the pan before landing. If your cap is really close to the pan, this increases the likelihood that the soot is depositing on your chimney instead of being carried away. 5) Are you in the open or in a sheltered space? Winds can help carry away soot as it leaves the chimney, and a well sheltered chimney can cause the soot to fall shortly after it leaves. Are you finding soot predominately in the direction of the prevailing wind? 6) Have you cleaned your chimney pipe (or had it cleaned) in the last year and a half? It is important, irrespective of fireplace/woodstove type, to have your chimney cleaned on an annual basis to remove creosote build-up. Just as the creosote can build-up on the glass of your fireplace doors, it builds up within the walls of the chimney pipe. This increases your risk of chimney fires. Many chimney cleaning companies will also provide a service to clean your brick/stone chase. There are also products available commercially so that you can do this yourself: (for example: http://www.fireplacemall.com/Chimney_and_Flashing_Repair/Chimney_Cleaner/chimney_cleaner.html) 7) Do you ever "douse" your fire in water? Remember, always damper down to extinguish your fire. Water increases creosote. Overall, how and what and where you're burning will have a huge impact on the soot staining of the stone on the exterior of your chimney. Keep in mind that light colors, porous stones and more textured faces will increase the visibility of the creosote buildup.

That is certainly a mysterious issue. We have something very similar with a part of a ceiling that keeps getting plastered and painted, and then it is disintegrating like water is still coming through, but just like you, our roof is new and the chances of leaking are slim to none. Condensation is a good idea. You might want to re-do the chimney entirely with something different for a covering. A lot of people are re-doing old chimneys by putting slab-type stones over them, and you could also brick it out with a new layer. There are also treatments that go directly over old brick to change the color or spruce it up if you wanted to go through the painstaking process of removing all the stucco. Maybe another commenter will have a better idea.