Cal. CCP § 1281.6

If the arbitration agreement provides a method of appointing an arbitrator, that method shall be followed. If the arbitration agreement does not provide a method for appointing an arbitrator, the parties to the agreement who seek arbitration and against whom arbitration is sought may agree on a method of appointing an arbitrator and that method shall be followed. In the absence of an agreed method, or if the agreed method fails or for any reason cannot be followed, or when an arbitrator appointed fails to act and his or her successor has not been appointed, the court, on petition of a party to the arbitration agreement, shall appoint the arbitrator.

When a petition is made to the court to appoint a neutral arbitrator, the court shall nominate five persons from lists of persons supplied jointly by the parties to the arbitration or obtained from a governmental agency concerned with arbitration or private disinterested association concerned with arbitration. The parties to the agreement who seek arbitration and against whom arbitration is sought may within five days of receipt of notice of the nominees from the court jointly select the arbitrator whether or not the arbitrator is among the nominees. If the parties fail to select an arbitrator within the five-day period, the court shall appoint the arbitrator from the nominees.