Va. Code § 15.2-1421
The governing body of each county may designate a tie breaker, whose duty it shall be to cast the deciding vote in case of tie, as set forth in § 15.2-1420. The designation of the tie breaker shall be by election by the voters of the county from the county at large. Every tie breaker shall serve for a period of four years from the date of his election and every tie breaker so elected shall serve the same term as a member of the governing body. No person shall be elected or serve as tie breaker who is not a resident of the county; who is not qualified to hold office as supervisor or who is an employee or officer of the county. Tie breakers heretofore appointed or elected shall continue in office until the expiration of the respective terms. Vacancies in the position of tie breaker shall be filled in the same manner as vacancies in the governing body.
Va. Code § 15.2-1421