For a time last spring, D.C. City Council Chairman Arrington Dixon was on the verge of realizing a politician's dream. It looked as if he might run unopposed for reelection to the city government's second highest office.

Now, six weeks before the Sept. 14 Democratic primary, his race has been transformed into a tough, uncertain contest for political survival against two opponents--one trying to resurrect a career that was derailed in 1978, the other giving up a secure seat on the council to break out of the obscurity of ward-level politics.

Former City Council chairman Sterling Tucker, who narrowly lost the 1978 race for the Democratic nomination for mayor, jumped into this year's council chairman contest in June after abandoning a second try for mayor as well as a once-discussed candidacy for an at-large seat on the council.

David A. Clarke, chairman of the judiciary committee and a member of the council from Ward 1 for eight years, entered the race for chairman in April, after reversing a decision made weeks earlier not to challenge Dixon.

Tucker, 58, is a veteran politician and former civil rights activist with high name recognition and a reputation for having run the council well from 1975 to 1978. He was slightly ahead of Dixon in a June poll taken by The Washington Post, but is regarded as a lackluster campaigner by many political insiders who wonder whether he started too late to put together an effective organization.

Clarke, 39, showed little name recognition outside his ward and trailed Dixon and Tucker in the poll. He has picked up some endorsements and is credited by his opponents with putting together a strong citywide orgnization.

"I think it is a tight race," said one influential city business leader and supporter of Dixon, who said he believes Dixon would have defeated Clarke in a two-way race. "Now any one of them can win." There is no Republican or independent candidate running.

While all three campaigns are are getting intense interest among politically active residents who have trooped through the summer heat to countless forums and campaign klatches, the race has been run in the shadow of the mayor's race and has not yet captured the attention of the general public.

"Most people are interested in vacations right now," said Marvin Tievsky, president of the Friendship-Tenleytown Civic Association in Northwest Washington.

The race for council chairman has always been an odd one in city politics. While many legislatures choose their leaders internally, the District of Columbia elects its at large, and the post has enough visibility, power and prescribed work to be more than the generally symbolic position of lieutenant governor in other states.

The chairman is more than a mere super at-large council member. He appoints committee chairmen, chooses key staff members who are paid high salaries and actually guides the city's legislative process.

He is the only one of the council's 13 members who is officially a full-time employe and because of that, his $51,290 salary is $10,000 higher than that of his colleagues.

In 1974, Tucker, who had served as vice chairman of the old appointed council, was virtually unopposed and became the council's first elected chairman. In 1978, Dixon won an election that many regarded as essentially a referendum on his chief opponent in the Democratic primary, Douglas E. Moore, who was then a controversial at-large member of the council.

This year, for the first time no candidate has become the focus of voter outrage and all three are experienced and proven city politicians, giving the race a new dimension. The overriding issue so far has been leadership of the council.

Many political and civic activists, council members and their staffs say Dixon, a 38-year-old former council member from Ward 4 in upper Northwest, does not have the political strength or talent to effectively run the council. Council sessions often are raucus, they say, Dixon doesn't control the debate and sometimes too many major bills are on the same session's agenda.

"We go out not knowing how he personally is going to vote on things," said one council member. Another, who heads a key committee, commented, "In almost four years Arrington has never come down to my office for a political strategy session."

Tucker says he can "put the council back on track."

"I want this office back because I can restore the leadership that I know this council needs," Tucker said recently. "I did not compete with my fellow council members." Tucker, who served as an assistant secretary in the U.S. Department of Housing and Urban Department after leaving city government in 1979, has for the past two years operated a consulting business.

Clarke also has pressed the leadership issue, regularly pointing out that giving up his council seat to run for chairman shows his determination.

"There are real and serious issues that face the city and the council and which, I believe, are reflected in the differences between the incumbent's record and my own," Clarke says. "We think we have the best platform," Clarke says, contending that Dixon "takes credit for everything good the council does and blames the council members for everything bad."

Dixon rejects such criticisms, saying some people mistake his "quiet, behind-the-scene" tactics for ineffectiveness. He tells audiences that the council in this political year has passed major legislation such as cable television and no-fault auto insurance, revised the city's liquor laws and approved redistricting of the city's eight political wards without a major battle.

Dixon argues that the support voiced for Tucker is partly "nostalgia for a former city official," and says Clarke doesn't have the smooth temperament for the job--two contentions that several council members also expressed privately.

Dixon blames much of the raucus debate that often mars council sessions on "upwardly mobile politicians who see me as a political threat and have their own political agenda."

He points out that four of the council members have mounted campaigns for mayor this year while Clarke and a few other members actively considered running for chairman.

Dixon and Clarke, who were surprised that Tucker got into the race so late, regularly point out at candidate forums that Tucker settled on the chairman's race after his mayoral bid failed. They tell audiences that the council is more independent now than when Tucker was its leader and that Tucker is trying to come back to a council that no longer exists.

Organizers from all three campaigns said they believe the winner will need about 40,000 to 45,000 votes from Washington's estimated 250,000 registered voters to win. Dixon said earlier this year he hoped to raise about $350,000 for the race, but a campaign aide said last week that figure may be too high. Both Tucker and Clarke had set goals of about $200,000 for their campaigns.

Clarke's organization says it has targeted pockets of voters around the city and hopes to gain a cushion of votes in Clarke's home ward, which includes Adams-Morgan, Mount Pleasant, Cardozo, LeDroit Park and parts of Shaw. Tucker said he has identified about 90 key precincts among the city's 137, and Dixon says he has ranked the precincts based on importance, but neither will be more specific.

"There was a lot of support for Mr. Clarke before Mr. Tucker came in," said Zelma A. Burt, a real estate agent and past president of the Northwest Boundary Civic Association in the Petworth community of Ward 4. "Mr. Dixon does a pretty good job, people just feel like he is not indepth enough."

Burt, who said she has no preference yet in the chairman's race, said Clarke "will do a better job than Dixon, but I don't know if he'll do better than Mr. Tucker."

Barbara A. Morgan, president of the Dupont Park Civic Association in Ward 7, said she felt "people will support the current administration--Barry and Dixon."

Albert Long, of the Benning Ridge Civic Association which also is in Ward 7 in Southeast, said he was supporting Clarke because of his anticrime stands, even though, he said, Clarke's name is "not a household word." "This is a predominantly black ward," Long said. "If he can get himself out, come to the ward and campaign, he can win." Clarke is white.

Georgetown civic leader Donald Shannon said Dixon hurt his chances in that wealthy area when he supported development along the Georgetown waterfront. He said Tucker "has some built-in support. But a lot of people are sentimentally for Dave Clarke."

Shannon noted that even though only six weeks remain before the primary, the race is still young. "There is not a lot of discussion," he said, "no passionate interest" in the race now.