Texas Labor Code - LAB § 102.014. Chairman

(a) The four arbitrators selected under Sections 102.012 and 102.013 shall designate a fifth arbitrator who serves as the chairman of the board.

(b) If an agreement as to a fifth arbitrator cannot be reached under Subsection (a), on notice of any arbitrator a district judge of the district that has jurisdiction over the dispute or grievance shall appoint the fifth arbitrator, who serves as the chairman of the board.