Because most birds within the United States are protected by the Migratory Bird Act of 1918, citizens cannot legally kill or relocate birds, their nests or their eggs. Scaring the birds off may work temporarily, but if the bird has an established territory around a house this isn't likely to work for long. The only steps that can be taken to stop the noise are steps to block it out.
Closing the windows may be one simple solution to blocking out the noise from singing birds. If the birds that are chirping have a short tree nearby that they like to perch on, the problem may be remedied by purchasing bird or deer netting and wrapping it around the tree. This would force the birds to find another perch.
In addition there are a number of noise-causing devices that could be used within a house to block out the chirping. A particularly loud fan may be able to block out the noise. A radio could also be used to play soft music or nature sounds, such as waves, a river or rain falling. A white-noise machine might also work to filter out the chirping.
It is illegal to intentionally harm the birds to get them to stop chirping.