If you search the internet you'll find many so called experts willing to test for damp with their meters, show you the high damp reading and happy to tell you that it's rising damp and you need an expensive liquid injection and two-coat render to tackle the problem.
The fact is, if there's no damp elsewhere in the property, it's a certainty that the damp around the chimney is NOT rising damp. What has happened is that, back in the days of actually burning coal and wood in the fireplace, tars and salts have leached into the brickwork. These salts are hygroscopic and put simply this means they absorb moisture. All the time. Hence the damp. And this damp can spread to adjacent skirtings and plaster. Whatever they tell you, rising damp treatment will not work.
How to treat it ? Ideally, you need to develop a flow of air through the chimney to offset the hygroscopic action. To do this fit an air brick around 200mm off the floor in the middle of the chimney and a cowl on the top of the chimney. If you also fit an air brick in the bedroom above you will also reduce condensation on the windows.
Alternatively, if the chimney has been plastered, another permanent solution is to strip the chimney back to brick where affected and either install a thin cavity drain membrane wrapped around the chimney or "tank" affected area with something like an Koster Aquatecnic sealant. Either of these treatments will totally stop any damp coming through and can be plastered to a fine finish.
I hope that's all clear and helpful. Regards John Answers Now Ltd