Boiling water will remove free chlorine, and at the same time it makes every other dissolved substance in the pot more concentrated, because water leaves as steam and the rest stays behind. Those two facts are usually presented separately, which is how people end up boiling water to improve it and quietly making one part of the chemistry worse in the process.
Removing chlorine and disinfecting are different jobs
Boiling is the standard household response to a microbiological risk, and it is effective for that. Removing chlorine is a side effect of the same action, not the reason a boil advisory exists. Conflating the two leads to odd conclusions, such as boiling water to strip the disinfectant and then storing it for days in an open jug, which removes the very thing that was protecting it.
What the residual is actually for
Utilities keep a disinfectant residual in the pipes so the water stays protected between the plant and your tap. Every community water system publishes an annual Consumer Confidence Report, and the EPA maintains a finder for locating yours; it names the disinfectant used and reports what was measured. Read it before deciding chlorine is a problem, because taste and risk are two different arguments.
What boiling concentrates
As volume falls, dissolved solids stay in the pot. Hardness minerals concentrate and deposit as the scale you see in a kettle. Nitrate, dissolved metals and most chemical contaminants concentrate too, so a long boil makes those slightly worse per glass rather than better. That is the reason boiling is never presented as a treatment step for chemistry, only for organisms.
Cheaper ways to get chlorine out
Activated carbon removes free chlorine reliably and continuously, in a pitcher, a faucet cartridge, an under-sink unit or a whole-house tank. For chloramine, catalytic carbon is the version to look for, correctly sized for the flow it has to treat. Either way the fix runs unattended for months, which is the point: nobody boils water twice a day for a year to improve the taste of coffee.
Questions people ask about will boiling water remove chlorine
Does boiling water remove chloramine as well as chlorine?
Not usefully. Chloramine is far more stable than free chlorine and a normal kitchen boil leaves most of it in the water.
Should I boil water to remove lead?
No, and it makes it slightly worse. Lead does not evaporate, so boiling concentrates it as the volume drops. Filtration certified for lead is the answer.
Is boiled water safe to store?
Store it covered, in a clean container, and use it within a couple of days. Boiling removes the residual disinfectant that would have protected it in storage.