Two things: you said that the chimney breast is entirely covered during winter with moisture. What that means is somewhere along the way moisture is getting under your shingles on the roof and draining down to your chimney and getting under the chimney breast.
When shingles do not keep out moisture, the moisture can freeze in Winter time, and the expanding ice from moisture shingle will push it farther out from its original, tight position. And more moisture can get in. In warmer months, the moisture trickles down the Roof and comes to rest around your chimney. The same thing happens: whatever moisture can get under the fixtures there can expand those fixtures and push them out. More moisture comes in, it freezes and expands, and any fixtures are no longer tight and must be fixed and re-seated. Including shingles.
Two, you might need a vapor barrier behind the wall to further protect it.
As for a contractor, find one that will give you a free evaluation. Do this with at least three contractors. Agree on the price and get that in your contract. Make them give you a detailed estimate including labor and supplies and a total cost. Then also agree how payments work: half now, half at the end? Payments? What are you comfortable with?
Make sure all of that is in your contract
What is the time frame? The contractor might be free on certain days or mornings or evenings. What should be finished when? What would they do to protect your house during absences? If the house is damaged, say from a thunderstorm or hail, what will they do to fix the damage caused by the bad weather?
All this should be in the contract.
We had a new roof installed, and while the roofers were gone, a thunderstorm destroyed one of the walls beneath.
The contractor said he'd fix it, but they couldn't give us the same material we had. It was wall board, a material thin as cardboard. You could thumbtack posters on it, which we sometimes did. They gave us the closest material to match the room: drywall. It was a step up from the wall board my Grandpa put up after WWII.
Look around on the web to see articles about questions you should ask contractors and what should be in the contract.
Good hunting!