This can occasionally happen, although it is rare. A chicken's beak will continue to grow throughout her lifetime, so as long as it is just the tip, her beak should grow back with no problems. Normally, her beak will slowly wear down with use, but if her beak grows faster than it wears, the tip may break, or a break can be caused by an injury. Possibly your chicken caught her beak somewhere and broke it trying to escape. In any case, check your coop and feeders to make sure there is no place to catch a toe or a beak just in case that was the issue.
If the break goes back very far, it can be very painful indeed. If her beak was caught somewhere, she may have other bruising, too, from trying to get unstuck. A break that is very far back may not grow back the same way, so it would be wise to consult a vet for large or dramatic breaks. Sometimes liver problems, certain types of mites or nutritional deficiencies can contribute to a weak beak. Your vet will be able to check her out and determine if there is some underlying issue. (The vet might be able to prescribe some pain medication, if necessary, too.) But sometimes there is no specific health issue--it can just have been an accident of some sort.
If the break is at the very edge, though, it's probably not painful, just disturbing, since she can't pick up things in her beak the same way as usual. The break itself, so long as it is the very end and she is able to eat, shouldn't present a long term problem, and if it is they very tip, will grow right back. Just watch to be sure she is eating and drinking as usual, since chickens will try to hide signs of pain and weakness. Even with a small break, take action if necessary and contact a vet if you suspect there is some underlying problem.
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