The Fairfax County Board of Supervisors voted unanimously yesterday to permit Straight Inc., a controversial treatment and rehabilitation program for teen-aged drug users, to establish its first chapter in the Washington area.

The privately funded program, which some critics contend is too hard on its patients, received a gushing welcome to the county from the nine-member board. "I'm very proud to have them in the county," Supervisor Thomas M. Davis III told Straight representatives and parents who crowded into the board room.

"We all at any time stand ready to help you in anything," agreed Supervisor Joseph Alexander.

About 140 families from the Washington area now send their children to a chapter of Straight in St. Petersburg, Fla., and they have raised $250,000 to bring the organization closer to home. More than 30 of those parents showed up for the public hearing to endorse enthusiastically the organization's appeal for a Fairfax location.

Ted Prophett, a Straight parent, explained to the board that a local chapter is needed because the program depends on family involvement. Young drug users, aged 12 to 21, spend between 10 and 14 months in the program, which emphasizes counseling by former drug users. Supporters claim a 60 percent success rate, which they say is unusually high.