CHICAGO'S MAYOR Harold Washington has finally gained control of a majority on the city's board of aldermen. We emphasize finally, because we reported erroneously April 25 that he had already done so. Mr. Washington's candidate in the key 26th ward, Luis Gutierrez, had at one point been declared the winner by the courts by a margin on the order of 20 votes. But we failed to note that the Chicago Board of Elections Commissioners, after the courts had ruled, found a handful of write-in votes, which denied Mr. Gutierrez an absolute majority. So he had to face a runoff against his opponent, Manuel Torres, last week.

That contest brought operatives loyal to Mayor Washington and to his archrival, Alderman and Cook County Democratic Chairman Edward Vrdolyak, into the mostly Puerto Rican 26th. It would be nice to report that the race hinged on high-minded principle. But a television debate between the two candidates featured charges that Mr. Gutierrez had been a sympathizer of a terrorist group in Puerto Rico and that Mr. Torres had been arrested for possession of cocaine, was behind in child-support payments and did not speak Spanish well.

It was a contest as Chicagoan as deep-dish pizza. But this time there was no question about the outcome. Mr. Gutierrez's margin was large enough -- nearly 1,000 votes out of 13,000 cast -- that Mr. Vrdolyak conceded defeat two hours after the polls closed. In the city where old-time Alderman Paddy Bauler once crowed after a famous machine victory, "Chicago ain't ready for reform," Mayor Washington now sounds a more tentative note: "They're just tired of the machine." It was a prudent response. The mayor now has an opportunity to show what he can do with control of the government. But no one doubts that whatever he does is just a prologue to what seems sure to be a fiercely contested election for mayor in the early months of 1987.