The gestation period for a chicken egg is 21 days - whether under a hen or in an incubator. For a more complete answer to the question, see the question and answer "How long does it take for eggs to...
Most eggs take about 34-35 days to hatch. The first egg laid takes about a day longer to hatch than the second egg (33 days). They hatch about 1.5 apart.
what you want to do after a egg hatches is put in a special incubator because they cannot make their own heat yet. make sure you feed them immediately after they hatch do not worry about feeding them...