Brookline Builders will repoint and rebuild your old chimney with Natural Lime Mortar. The reason most chimneys fail is because of water penetration. If a cap of either flagstone or metal is maintained and installed on your chimney, the water will not penetrate and your chimney will outlast the roof. If water is not kept out of your chimney it will deteriorate extremely fast, especially in the winter during freeze thaw cycles. If your chimney needs to be rebuilt don't ever use portland based mortar, especially on a chimney.
Portland will not withstand the expansion and contraction of an exposed chimney, it will crack quickly then fall apart in just a few years. This is because portland based cements are water proof, so once the water penetrates into the chimney, and it will, the portland does not allow the moisture to escape. This moisture that is trapped in the exposed chimney will expand when it freezes and thaws. Over a few years the effect of this cycle the chimney will blow apart.
The key to repointing an historic chimney is to not use any portland cement. Rather use natural lime mortar. Natural lime mortar will allow trapped moisture to quickly escape and will self heal any cracks. The pyramids in Egypt were built using natural lime mortar. Portland cement wasn't widely used in the US until the early 1900's.