my own experience with chalkbrood mirrors what Jim said. It can be viewed as similar to wax moth or beetles as an issue. It seems it is always there dormant- waiting for the right conditions to take hold. I have observed here in Adelaide that it is a seasonal thing. Last year in spring and summer we had a bit of it in many hives. This year hardly any at all. The best defense against it is to build up strong hives.
I have been told that it is related to chilled brood, so the best way to stop it is to make sure that hives are kept full of bees. That means not putting supers on until the box below is packed with bees, not transferring nucs into bigger hives until they are strong and crowded, taking care with checkerboarding frames and only doing it during good weather and with very strong populations. It might mean moving a hive out of a shady and/or damp position.
A month ago I had a strong hive that had no chalk brood at all. I went into the brood box and found the outer two frames were all honey and pollen. I decided to remove them and also one frame of eggs to donate to a queenless nuc. I checerboarded the new foundation frames into the brood box. Two weeks later I observed some chalkbrood mummies being thrown out of the front of the hive. It seems I went too far breaking up the brood cluster and the brood got chilled allowing the chalk brood to get a hold. In spring I could have down the same without any issue- but things had slowed down and we have had a very cool summer. As that hive is still very strong I expect it will soon recover.
At times a weak brood box with chalk brood would be better off condensed down into a nucleus until it builds back up.
Some people place a banana cut in half length-ways on the top of the brood frames to stimulate cleansing behavior. Others believe it is a gas that the banana gives off that inhibits the chalk brood spores. I have tried it but can’t really say that it helped- it may have I am not sure.
others say that if a hive doesn’t recover over time re-queening may help- as the original queen may have lacked sufficient hygienic behavior.
The good news is that in the end chalk brood generally just disperses if the colony is kept strong.