I have 2 stone block chimneys that have a few pieces that have fallen off, otherwise they seem to be in OK shape (from 1959). My question is - are you supposed to apply a waterproofer to the exterior of the chimney from time to time? Or is that not something that is typically done or recommended?

Thanks

2 stone block chimneys
Is this an actual real stone veneered chimney?
Yes you should check all stone pointing around that chimney and look for hair line cracks. Over time they develop and its not easy to see. If this is a stone veneered chimney and not a solid one it's a natural form of siding I'm a mason/stone mason and I have a hard time convincing customers the importance of sealing a masonry wall as it gets older. Every body think oh its stone or brick. Well mother earth beats on that and where does our dirt come from besides decay of plant and animal, ROCKS and sea .
Check the rest of the chimney and you may be very surprised what the mortar joints look light right where it tolled against the stone. Now If need more repair and more stone relayed Find a mason and a good one. If he has to ripp some of it down here's the approach that's needs done.

Take many close pictures of how the stone is laid. Just one stone off in a couple of feet of chimney will mess up the whole job. Its not easy to get natural stone to match. Here is the other important part. When the stone is laid and he goes to strike/tool it if that is done to early on the mortar joint being to wet the lime will come to the surface and bleach it more and won't match the old mortar to well
And yes seal the chimney after 30 days of repair or next spring

Signed 21 Boat

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Thanks for the great information. I will seal it this spring.