The Fairfax County School Board voted after more than two hours of closed-door debate to retain its internal power balance by reelecting its chairman and vice chairman.

With little opposition, chairman Ann P. Kahn was named to a third term as head of the 10-member board. Vice chairman Mary E. Collier was narrowly chosen over board member Robert E. Frye.

In past years, the board has been heavily criticized for selecting its leaders in secret sessions. Kahn said last night that the board took no actual votes in its closed meeting this year but conducted a "roundtable discussion" to gauge the positions of board members.

Under Virginia law, the board can discuss such appointments in closed meetings, but must take official votes in public.

Kahn won on a vote of 8 to 1, with board member James W. Kitchin casting the only vote against her. One member was absent.

The more heated contest was for the vice chairman's slot. Several board members said they entered the closed meeting intending to seek the office, but there were votes for only two candidates when the members met in public session two hours later. Collier, seeking her second term as vice chairman, won on a 5-to-4 vote.

Last year Frye, the board's only black member, threw his support to Collier in secret session after the two tied in a runoff.

The board last night also repealed a recently approved 10-cent increase on school lunch prices for next year. School officials said profits from lunch sales were three times more than expected at the end of this year. The board had originally expected that the increase would be made necessary by cutbacks in federal funding, inflation and reduction in lunch sales.

School officials said a new approach in selling lunches that allows students to purchase items a la carte boosted sales. In addition, expenditures for food and salaries were lower than expected, and the federal government cutbacks were not as severe as anticipated.

Student lunches will remain 75 cents in elementary schools and 85 cents in intermediate and high schools. Adult lunches will remain $1.30.