An Important Notice has been issued under Section 215 of the U.S Immigration and Nationality Act (INA):

It is illegal for U.S. citizens to enter or leave the United States on anything other than  their U.S. passport. This rule also applies to dual US citizens,  for example, if you have both an Irish and U.S. citizenship, then you  MUST enter and leave the United States on only a valid U.S. passport; you may NOT enter or depart the United States on your Irish or foreign passport. This rule strictly applies also to your children if they are either US citizens or dual US citizens.