Arlington County Board Chairman John G. Milliken said yesterday that he will not run for Congress this year in Virginia's 10th District, leaving no clear Democratic challenger to four-term Republican Rep. Frank R. Wolf.

Although Milliken ran against Wolf in 1986 and was beaten by a ratio of 3 to 2, officials in both parties considered him the leading Democratic contender and said Wolf is now in an even stronger position for reelection this fall.

"For me the question was and is in 1988 what is the most effective way that I can contribute," said Milliken, noting that he plans to run for a third term on the county board this year. "I decided I could really do better where I sit rather than running a campaign against a well-known incumbent."

He said if the seat for the 10th District, which includes Arlington County and part of Fairfax County, had been an open one, "my conclusion might have been different."

In addition to working on local housing and transportation issues, Milliken said he would take a major role, either as state chairman or cochairman, in the presidential campaign of Massachusetts Gov. Michael S. Dukakis.

Milliken's decision not to run came as good news to already confident Republicans. "Frank Wolf begins as a heavy favorite for reelection," said Arlington Republican Chairman Scott McGeary. Milliken was considered by many to be a legitimate contender because he had name recognition from his time on the Arlington board and his exposure during the 1986 congressional campaign.

"The prospect of having a new challenger would make Frank even more of a favorite," said McGeary.

The Democrats "usually come up with someone" to challenge Wolf, said James D. Swinson, the Fairfax County Republican chairman. "Let them go ahead."

Some Democrats have expressed interest in the race, but none has made a move. Even possible candidates sound less than optimistic. "Wolf is a formidable opponent," said state Sen. Charles Waddell, who represents parts of Fairfax and Loudoun counties.

"He's provided good constituent services and kept his fences mended. He would be difficult to defeat," said Waddell.

He added that it would also be tough to raise the money needed to mount a strong challenge. "Starting this late in the game, raising $1 million, that's something that would give you pause . . . . I'm leaving the door open {to a candidacy}, but just barely," said Waddell.

Another possible candidate named by party officials is Harris Miller, chairman of the Fairfax County Democratic Party. He was more upbeat about the chances of beating Wolf.

"Any incumbent is difficult to defeat, but there are some different factors this year," he said, pointing to the presidential election and the Senate candidacy of former governor Charles S. Robb. Both are expected to increase the Democratic turnout.

Don Beyer, a local Volvo dealer and major Democratic fund-raiser, said it would be difficult for any challenger to raise large amounts of money to oppose Wolf. Milliken "was the last great hope," he said, "and people invested heavily {in the 1986 campaign}, to the tune of about $800,000."

Fund raising "will be much harder in the wake of John's defeat" two years ago, he said.

With Milliken out of the race, the field of potential candidates is almost nonexistent, said one Democratic activist. "You got me," said Arlington Deputy Treasurer Kevin R. Appel when asked to name a Democrat who will challenge Wolf. "I would say nobody, but who knows."