Probably the birds you hear are nesting in your chimney, and they’re right where they want to be. The most likely possibility is that the birds are Chimney Swifts (assuming you live within their range in eastern North America). If so, the young will have no trouble at all leaving the chimney. It’s possible they’re European Starlings, which commonly nest in cavities and crevices in buildings. Those young aren’t as adept as swifts, but they’re still likely to be able to fly safely out of the nest when it’s time.
Sometimes, larger cavity-nesting birds like Wood Ducks and Barn Owls can fall down into a chimney and are too large to fly out, but these would make quite different sounds than a nest full of chicks. If you have a traditional chimney, you can try turning off all the lights in the house, leaving a door open and opening the flue—the bird will see the light of the exit and try to get out. If that fails, it is best to contact a licensed rehabilitator; you can find one in your area here.
Make sure you don’t use your fireplace until you are sure all birds have left your chimney.
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