Swifts

Vaux's swifts often build nests on the insides of house chimneys, and are known for their loud chirping. The babies often fall out of their nests, or the nests will fall apart and the babies will end up inside fireplaces. Fortunately, these birds have extremely sharp claws that help them cling to the brick inside a chimney. If you can reach up inside your chimney past the flue lining (which is slippery metal that a bird cannot cling to), a displaced baby can grab a hold and will climb back up inside where the parents will come down to feed it. After placing a baby inside the chimney, close the flue so that it won't fall down into the fireplace again. Another alternative:

Fashion an artificial nest using a plastic container as described under "Baby Birds."
Attach one or two extended coat hangers to the artificial nest.
Bend one end of the coat hanger into a U shape and hang it over the chimney lip at roof level so that the artificial nest is lowered down inside the chimney. (This is of course assuming that you can safely climb up on your roof.) With this nest, the parents can get to their babies and the babies will still be able to climb out onto the chimney when they get older.