D.C. City Councilman Arrington Dixon officially entered the race for council chairman yesterday, saying the city could not afford racial polarization, the "rhetoric of negativism" and the flight of its taxpayers to the suburbs.

Dixon's announcement made from the porch of the historic Frederick Douglass home on Cedar Hill overlooking the rooftops of poverty-ridden Anacostia, set the stage for what is expected to be a lively - and perhaps bitter - contest for the post between himself and maverick Democratic Councilman Douglas E. Moore.

The 35-year-old Dixon never mentioned Moore - the only other candidate in the race - by name. At several points in his speech to about 200 persons gathered on the raindampened grounds, however, it seemed clear that he planned to paint Moore as a man of little work, divisive intentions, narrow interests and insufficient political support who should not run the city's legislature.

"Anyone who assumes the office of the chairman, with any serios intent of delivering to the people of this community, has got to have a commitment to working with others," Dixon said. "The chairman of the City Council is not an office for the Lone Ranger.

"No amount of words will make the goals of our community happen . . . Words may excite you and fill your stomachs, your pockets or your days. That's why my tenture on the City Council has been spent on work - not just words."

Dixon made no specific legislative proposals, but spent significant time supporting the need for a city-run lottery as a means of lessening the burden of city taxpayers.

"I understand the concerns some folks have about this issue, but if we want our children to have the properly financed quailty education they deserve, we have got to stop the flow of the hard-earned money of the District of Columbia into the Maryland treasury," Dixon said. Maryland now runs a daily lottery, which may District residents play.

"You know and I know that 'The Lord helps those who help themselves.' So let us help the Lord help us by helping ourselves to all that revenue that goes into Maryland and belongs to us," he said.*TDixon also said "every segment of the society" had to be encouraged to remain in the city, jobs had to be developed for the city's youth, working relationships with regional neighbors improved and education, city services and crime prevention efforts made better.

Although Dixon has endrosed present Council Chairman Sterling Tucker for mayor, Tucker was not at Dixon's campaign kickoff yesterday. Several key persons in the Dixon organization said Tucker will probably not endrose Dixon.

Instead, they said. Dixon will probably draw support - if only by declarations of neutrality - from all three of the major Democratic mayoral contenders - Tucker, Mayor Walter E. Washington and council member Marion Barry.

That kind of interlocking support already appears present in the Dixon organization. For example, D.C. Democratic State Committee Chairman Robert B. Washington Jr., a strategist and fund-raiser for Tucker, will do the same for Dixon. Realtor Flaxie Pinkett, a long-time friend and expected fundraiser for the mayor is cochairman of Dixon's finance committee. Council member Polly Shackletan (D-Ward 3), who leans strongly toward Barry, will also be working for Dixon. For months, many in the city's business and professionals communities, regular Democrats and others, had fretted over the lack of opposition to Moore, who announced his candidacy Sept. 18. If Moore were elected, these persons feared, the city could have a "rabble-rousing" image, blacks and whites would be divided and businesses would be driven away at at a time when the city appears on the edge of one of the biggest commerical building booms in the past three decades.

Opponents of Moore were concerned that some of the best possible challengers to him were interested in running either for higher office - such as mayoral hopeful Barry -or for no offices at all - such as the pastor of all souls Unitarian Church, the Rev. David H. Eaton.

In addition, they feared that Moore's hard driving and aggressive political style as well as his uncanny choice of support for seemingly divergent issues - he is for rent control and against gun registration, for example - would be a hard match to beat in the unpredictable politics of a city that recently won home rule.

Dixon's campaign strategy, as explained in a lenghty interview Friday and in talks with several of his advisers, appears to be one of not taking on Moore in a continuing head-on verbal contest, and not hammering away directly at Moore's record in office or his well-publicized scrapes with the law.

"If the community knows certain things, then why do I have to spend time, energy and resources of hard working campaign workers and supporters to say thing that people already know?" Dixon said.

Instead, Dixon plans to spend most of his time projecting his image as one who is "stable, consistent, predictable" and "responsible."

"There's only one problem in this campaign. And that is to get the resources to present the community the kind of public servant that Arrington Dixon is," he said.

Dixon said to convey that message his organization will have to spend "in excess of $200,000" - more money than Mayor Washington reported spending for election to the city's highest local office in 1974. Moore said he plans to spend less than $10,000.

More than half of those funds, Dixon said, will go into a media campaign. Cameramen were on hand at yesterday's rally staging shots of children wearing green-and-white "Dixon for Chairman" buttons with the candidate in the background. The Dixon organization had already commissioned a $13,000 poll, which Dixon said will deal more with image than with issues.

The prospect of a $200,000-plus campaign g for the number two job city government comes at a tine when all three major mayroal candidates are talking of raising about $200,000 or more. That would mean there are plans to spend nearly $1 million in this fall's elections.

Dixon acknowledge that one of his current weaknesses is name recognition. He has twice been elected to the council from the mostly upper income Ward 4 in Northwest Washington, but has never run or held citywide office. Moore, on the other hand, was elected to an at-large council seat in 1974 and received more votes than any of the 16 other at-large candidates in the general election.

Dixon's Anacostia announcement was a first step toward the necessary expansion of his political base. He chose that site, he said, because it is not far from where he was born and reared. It is also one of the poorer black sections of the city, in contrast to the ward he represents on the council, which is considered by many to be the home of the city's most affluent blacks.

Dixon said he does not plan to pitch his campaign toward any special segments of the city. "I think the majority of the prime voters (in the city) would be supportive of the kind of candidacy that I represent," he said.

Also present at Dixon's announcement was D.C. Denocratic National Committeeman John W. Hechinger, the Rev. Willie B. Allen of Upper Room Baptist Church (who knew Dixon as a child and said he was not there to endrose his candidacy), Thomas J. Owen, president of Perpetual Savings & Loan Association and Vivien Cunningham, former director of Southeast Neighborhood House and Dixon's campaign chairman.

Moore was not present but later had a response to Dixon's announcement. "I love his opening shot because it was a popgun. It is true he has been working, he has worked well to serve the special interests of the city," said Moore.

"My mother named me after Frederick Douglass," he said. "Frederick Douglass must be turning over in his grave, for one who has served the special interests to come to those hallowed grounds."