David, this is something for which you should seek the advice of a local heating pro. Fortunately, there are plenty of local heating contractors (whom I expect inherently work on fireplaces/chimneys) seeking to give free estimates with no obligation, and taking advantage of this is the consumer-smart way to go about finding an accurate answer to your question. It’s important that you get a local estimate and not rely on guesses found here on Yah, as a lot of factors really bear on the cost of such a project, including the following: The cost of material and labor greatly varies by location.

As I said, Free estimates from local heating contractors are the key to your success in this home improvement project of yours. Here’s a great link to a handyman site that offers free very resourceful information to assist you in determining the cost of your project, and, ultimately, selecting a local heating contractor in an effort to get the best deal for you:

HEATING CONTRACTOR INFO:

http://yourhandymanzone.com/Your_Handyman_Zone_Free_Estimates_Heating_Cooling.htm

I’m sure you’ll find the information you need, specifically the tips, useful as it relates to being treated fairly by contractors and exploring the consumer-wise approach of getting free written estimates to find the best contractor in your area.
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Source(s):
The Internet is what I use. I’m pretty knowledgeable about the Internet. I have a firm belief in helping people with what I know, including from my development of sites, such as the one cited above. Sharing really is caring, and I wish those who I help can reciprocate by sharing what they know.