(a) Within five (5) days from the expiration of the thirty-day (30) period referred to in § 28-9.5-7, the bargaining agent and the state authorities shall each select and name one arbitrator and shall immediately notify each other, in writing, of the name and address of the person selected.
(b) The two (2) arbitrators selected and named shall, within ten (10) days from and after the expiration of the five-day (5) period above, agree upon and select and name a third arbitrator. If, on the expiration of the period allowed, the arbitrators are unable to agree upon the selection of a third arbitrator, the chief justice of the Rhode Island supreme court shall select a resident of Rhode Island, or a person whose place of business or principal place of employment is in Rhode Island, as the third arbitrator upon request, in writing, from either the bargaining agent or the state authorities.
(c) The third arbitrator, whether selected as a result of agreement between the two (2) previously selected arbitrators or selected by the chief justice, shall act as chairperson of the arbitration board.