If the chimney is structurally sound, you may be able to (3) re-line it. There are several ways that this process is done. Various contractors each have a favorite way that they generally use.
We also have a favorite method, and we think it has advantages over the alternative methods. It is fairly easy to do and reasonably economical, and it produces a very safe chimney, and even makes it stronger than it was to start with. Most "handy" people could probably do it themselves, but they should have an expert check their finished work.
Here's the method we recommend:
The chimney is cleaned. Next, a single-wall stainless steel
inner liner is lowered down from the top, connecting
sections as you go. There are even flexible sections available for
chimneys that have curves. (Some re-lining contractors just do this,
and it actually IS an very acceptable way to re-line a chimney).
Our preferred method continues with making a temporary "plug"
at the bottom of the chimney at the damper location, around the new
liner. This temporary plug could be plywood or metal, because it would
soon be removed after the THERMIX concrete sets. Next, a special
material called THERMIX is mixed with water (it comes in a bag as at
right) and poured down outside the liner. This TherMix is a combination
of vermiculite (non-combustible) insulation and a concrete mix.
Pour a little first (a couple feet deep), to form a permanent TherMix/concrete plug at the bottom. Then a day later, the rest gets poured in up to the chimney top. As the material is poured in, it's usually good to vary the pouring location, to keep the stainless steel liner in the center of the original chimney.
The stainless steel inner liner eliminates deterioration. The TherMix vermiculite insulation keeps chimney heat from escaping through the sidewalls of the chimney to any nearby wood structures, making the chimney safer. The TherMix concrete make the chimney physically stronger than before. The insulation even helps the chimney stay warm better so the draft is more consistent! The fireplace is likely to even burn better than before!
For your information, some re-lining contractors use only the TherMix to re-line the chimney. They use a heavy-duty hot-dog-shaped balloon to maintain the final chimney opening. After the TherMix sets, the balloon is deflated and removed.
We just think that combining both methods is not much more expensive, and it has so many long term benefits, that it is worth doing both. The TherMix material for a normal sized chimney is a few hundred dollars. A stainless steel liner is also a few hundred. Compared to the cost of an entirely new chimney ($$$$$$$), re-lining is an attractive alternative. We believe you should consider the extra few hundred dollars to do both versions, for added safety of the house and better burning characteristics of the fireplace. Considering that the fireplace originally cost several thousand dollars, springing for a few hundred more here seems like a reasonable investment.