sal2014,

That would depend a lot on the house. If you don't do it, what would happen to the chimney?

You would be better off asking a realtor in your area.

Why does the existing chimney have to be destroyed? It is usually possible to repair a brick chimney and would be far cheper than tearing down and building anew. I'd be a little suspicious of the tear down and rebuild proposal.

I agree a realtor could probably answer your question, but as rough guess I'd say a working, safely lined chimney would add at least $10k in value. If it had a hearth, either alone or as part of a fireplace, probably $20 to $25k.

The value of house is depend on their quality and design. You can tell the possible buyer that you invest in chimney to make a good deal with it. However, sales-talk is the best strategy to sell your house quickly.

Here is a link that might be useful: Cheap Home Builders

A house is more desirable with a fireplace, but you don't need a chimney to have a gas fireplace - you can direct vent through the wall. I doubt that your average buyer would even notice that there wasn't a chimney.

You can put a liner in an old chimney and use that to exhaust a gas fireplace.

I'm very suspicious of a "no good" chimney diagnosis. Chimneys can be relined cost effectively.

1) I'd be surprised if your existing chimney couldn't be repaired more cost effectively than replacing it. I'd get a second or third opinion.
2) With modern furnaces and HW heaters you don't need a chimney at all, indeed sealed combustion units that draw in outside air and exhaust through a PVC pipe are much more efficient and safe against potential backdraft situations.
3) If your chimney is a major architectural feature of your house than it will probably be a detriment to remove and not replace it.
4) If you want a fireplace you need a well functioning chimney. If your existing chimney has non-structural problems either a stainless steel or concrete liner can be fitted to make it work again.