It depends. The N-400 naturalization application specifically asks, “have you ever failed to support your dependents….” You must be able to answer this question truthfully. Child support delinquency can be overcome by catching up on the payments and asking your ex to write an affidavit about how you made amends. If you willfully failed or refused to support you dependent child during the 5-year period before you applied for U.S. citizenship, you will have to show extenuating circumstances that contributed to that decision.