Va. Code § 15.2-802
The powers of the county as a body politic and corporate shall be vested in an urban county board of supervisors, to consist of one member from each district of such county and to be known as the board of supervisors (the board). Each member shall be a qualified voter of his district and shall be elected by the qualified voters thereof. In addition to the above board members, the voters shall elect a county chairman who shall be a qualified voter of the county. No person may be a candidate for county chairman at the same time he is a candidate for membership on the county board from any district of the county. A quorum shall consist of a majority of the board and the chairman shall be included and counted.
The county chairman shall be the chairman of the board and preside at the meetings thereof. The chairman shall represent the county at official functions and ceremonial events. The chairman shall have all rights, privileges, and duties of other members of the board and such others, not in conflict with this article, as the board may prescribe. In addition, the chairman shall have the power to (i) call special meetings of the board in accordance with the procedures and restrictions of § 15.2-1418, mutatis mutandis; (ii) set the agenda for board meetings; however, any such agenda may be modified by an affirmative vote of the board; (iii) appoint county representatives to regional boards, authorities and commissions which are authorized in advance by the board; however, any such appointment shall be subject to revocation by an affirmative vote of a majority of all members elected to the board acting within the 30-day period following that appointment; and (iv) create and appoint committees of the board and name presiding members of such committees as authorized by the board; however, any such committee or appointment shall be subject to revocation by an affirmative vote of a majority of all members elected to the board.
At the first meeting at the beginning of its term and any time thereafter when necessary, the board shall elect a vice-chairman from its membership who shall perform the duties of the chairman in his absence.
The supervisors and chairman first elected under the provisions of this chapter shall hold office until January 1 following the next regular election provided by general law for the election of supervisors. At such election their successors shall be elected for terms of four years each.
If the number of districts in any such county is increased by redistricting or otherwise subsequent to a general election for supervisors, and such supervisors have taken office, then the board shall adopt a resolution requesting a judge of the circuit court for such county to call a special election for an additional supervisor or supervisors in accordance with the increase in the number of districts, such additional supervisor or supervisors to be elected from the county at large, and such election shall be held within 45 days from the date of such request. The qualifications of candidates and the election shall be as at general law applying to special elections. Any supervisors thereby elected shall hold office until January 1 following the next regular election provided by general law for the election of members of the board, and at the next regular election all supervisors of any such county shall be elected from districts as provided by law.
If a vacancy occurs on the board, the chief judge of the circuit court for such county shall call a special election, in the district if the vacancy is of a district supervisor, or in the county at large if the vacancy is of the chairman, to be held not fewer than 45 nor more than 90 days after the occurrence of the vacancy; however, if the vacancy occurs within 150 days prior to a general election, such special election may be held on the general election day; and if the vacancy occurs within 120 days prior to the date of a regular election for the board of supervisors, such vacancy shall be filled by appointment by the remaining members of the board within seven days of the occurrence of the vacancy, which appointment shall be for the duration of the term of office of the person whose absence from the board occasioned such vacancy. The qualification of candidates and the election shall be otherwise as at general law applying to special elections.
Va. Code § 15.2-802