Harold Washington's mayoral victory in Chicago brings back memories of the decade of the '50s when this reporter was covering politics there. Item: The forecast in a national magazine article by a population expert that Chicago would have a black mayor by the 1980s. The prediction was greeted with hoots of derision from the city's political pundits. They saw politics remaining much the same indefinitely, with blacks given little more than a bit of patronage in return for helping elect white Democratic mayors.
Item: The hard-fought campaign in which Republican reform candidate Robert Merri-am sought to turn back Richard Daley's first bid for mayor. Merriam, an attractive candidate who picked up independents as well as Republicans, at first looked as if he might be the winner. But then the black wards began to come in with massive votes for Daley. The black leaders had once again delivered for the Democratic candidate. It was all over.
Item: The aftermath of the Daley victory. In the early hours of the morning, as the tide was turning against Merriam, one of the old-time white ward leaders, Paddy Bauler, mounted a victory party table to dance a jig and shout at the top of his voice, ''Chicago ain't ready for reform yet.''
Now we are into the '80s and a black mayor is at the helm in Chicago. Blacks at long last have broken a pattern in which they had acted pretty much as lackeys to white political bosses. Although real reform may be some distance away, there are signs that the old system is finally beginning to splinter. A federal judge has issued an order that specifies certain steps which Chicago must take to end political favoritism in hiring.
In confronting the old Daley machine, Harold Washington has an opportunity to bring a cleaner political atmosphere to the city. He talked earlier of blacks having ''their turn.'' This seemed to signify that the old white machine might be replaced with a Washington black machine, with patronage for blacks. But as Washington seeks to bury the bitterness of the campaign by ''reaching out my hand in friendship to every living soul in this city,'' he may see this as the moment to breathe more equity and honesty into the way the city is run.
Some Republicans believe that more than racial politics was involved in the strong run of GOP candidate Bernard Epton: They think that the Democratic machine at long last is crumbling and that Democrats who voted for Epton will in the future find it easier to vote Republican. Perhaps. It remains to be seen what comes next in Chicago's turbulent politics.
Should Washington fail to achieve the unity he seeks, some other scenarios might be written. For example, an adviser to the Reagan administration says that Washington's victory will be ''good'' for the Republicans - that Washington will now hasten a flight of city whites to the suburbs where they will tend to give up their old Democratic ties and become Republicans.
Such a white flight, which has been occurring in some other big cities, would leave the Chicago mayoralty to the nonwhites while bolstering the Republican vote in state and national elections. It could also lead to the decay of the inner city.
But in the past Chicago has been known as a city that ''works,'' where whites have stayed and lived alongside blacks - though not without flareups and incidents. Wouldn't it be a victory for Chicago - and the nation - if the new Chicago mayor found a way for blacks and whites not merely to coexist but to live together in more harmony?