Del. Code tit. 22, § 321

The legislative body of cities or incorporated towns shall provide for the appointment of a board to be known as the board of adjustment and in the rules and regulations adopted pursuant to the authority of this chapter shall provide that the board may, in appropriate cases and subject to appropriate conditions and safeguards, make special exceptions to the terms of the ordinance in harmony with its general purpose and intent and in accordance with general or specific rules therein contained.