Del. Code Ann. tit. 10, § 5805
(a) The Court of Chancery of the State, on petition or on application of a party in an existing case, has exclusive jurisdiction to appoint 1 or more arbitrators upon:
Following the petition or application, each party shall propose to the Court of Chancery no more than 3 persons that are qualified and willing to serve as an arbitrator.
(b) (1) The Court of Chancery shall, within 30 days of the service of the petition or application, appoint an arbitrator and, in so doing, may take into account:
(2) An arbitrator appointed by the Court of Chancery may only be:
An arbitrator so appointed has all the powers of an arbitrator specifically named in an agreement. Unless otherwise provided in an agreement, the Court of Chancery shall appoint a single arbitrator.