21st Century Child Care Investment Act This bill amends the Internal Revenue Code to allow a tax credit for employment-related expenses for services provided by a high quality child care center. The credit applies to taxpayers with adjusted gross incomes below specified levels and is limited to: (1) $14,000 for each qualifying child who is under the age of three by the end of the year; and (2) $5,000 for each qualifying child who has attained the age of three by the end of the year, with adjustments for inflation after 2017. A "qualifying child" is a dependent who is under the age of five. The care must be provided by a facility that: (1) receives a fee, payment, or grant for providing care for children (other than just children who reside at the facility and regardless of whether such facility is operated for profit); and (2) meets state licensing requirements. For taxable years beginning more than five years after enactment of this bill, the facility must also: (1) meet high quality rating requirements under the quality rating and improvement system of the state in which the care is provided, and (2) be certified by the Department of Health and Human Services. A portion of the high quality child care tax credit is refundable, depending on the adjusted gross income of the taxpayer. The Department of the Treasury must establish a program to, at the election of the taxpayer, make monthly advance payments of the credit directly to a high quality child care center. The bill also makes a portion of the dependent care tax credit refundable.