The Arlington Democratic Party last night nominated John G. Milliken, a 34-year-old Washington lawyer and former county Democratic committee chairman, for a seat on the five member Arlington County board.

Milliken, a former aide to Northern Virginia Democratic Rep. Joseph L. Fisher, will face John Simone Pace, a 39-year-old vice president of Washington Blue Cross, who will run as an incumbent with Republican endorsement in the November election. The two are competing for a seat being vacated by John W. Purdy.

No matter who wins in November, power on the board will remain with the three-member Republican-backed majority for the next three years.

Milliken easily won nomination last night over Julius Brenner, an Arlington baker.

The chief issue at last night's meeting, attended by more than 270 persons, was whether Milliken should run as a Democrat or follow tradition and run as an independent with the joint endorsement of the Democratic party and the nonpartisan but overwhelmingly Democratic Arlingtonians for a Better County organization.

Because of Arlington's large population of federal workers who are barred by the Hatch Act from participating in partisan political campaigns, Democratic candidates have run as independents for more than a decade. Last night's decision leaves unclear the future of the 25-year-old Arlingtonians for a Better County organization, one of the oldest and most effective reform movements in the United States.