710 ILCS 5/3

If the arbitration agreement provides a method of appointment of arbitrators, this method shall be followed. In the absence thereof, any method of appointment of arbitrators agreed upon by the parties to the contract shall be followed. An arbitrator so appointed has all the powers of one specifically named in the agreement. When an arbitrator appointed fails or is unable to act, his successor shall be appointed in the same manner as the original appointment. If the method of appointment of arbitrators is not specified in the agreement and cannot be agreed upon by the parties, the entire arbitration agreement shall terminate.