13 Del. C. § 507

(a) The Family Court of the State shall have exclusive original jurisdiction over all actions arising under this chapter. The Court shall have exclusive jurisdiction over the construction, reformation, enforcement and rescission of agreements made between future spouses, spouses and former spouses concerning the payment of support or alimony, the payment of child support or medical support, the division and distribution of marital property and marital debts and any other matters incident to a marriage, separation or divorce. The Court shall have jurisdiction to resolve any issues resulting from the construction, reformation, enforcement or rescission of an agreement. In this regard, the Court shall apply the statutory factors set forth in Chapters 5, 6 and 15 of this title. The Court shall have and exercise all other jurisdiction and powers relating to support and separate maintenance actions heretofore possessed by the Chancellor or the Court of Chancery of the State.

(b) The jurisdiction of the Court of Chancery in civil actions for separate maintenance is hereby terminated, except for such actions for separate maintenance as have been commenced in the Court of Chancery prior to the effective date hereof. The Court of Chancery shall retain exclusive jurisdiction over such latter actions.