TRY AS HE may -- and already has -- Mayor Barry cannot hide the fact that his fire chief should go. For whatever reasons, none of which hold up against the record, Mr. Barry has continued to keep Theodore Coleman in this job. The result has been a series of embarrassments involving the fire department in general and the emergency ambulance service in particular. Were it merely a matter of misadministration, the mayor might still try to improve things without ousting the chief. But Chief Coleman has been more than a poor administrator; he has been an obstacle between earnest efforts by subordinates to improve services and the top ranks of the executive branch, where decisions and policies should be supported and/or enforced.

This is hardly a new development. Over the past few years, Chief Coleman has been criticized from many corners on a wide range of issues:

Allegations of poor training of emergency crews: paramedics, rescue divers, how to get around town, what to do when they get there.

Continued use of faulty equipment.

Orders to firefighters to dig the chief's car out of the snow last year.

Failure to support or cooperate with the director of ambulance service -- the ninth such director since the mayor appointed the chief in 1982.

Obviously some of these issues are more important than others -- starting with the shocking state of ambulance services, with nine reported incidents of people dying after ambulances were too slow in reaching them. Even though no official link has been made between the deaths and delays, the accounts of ambulance responses in these cases are riddled with terrible mistakes. With only two hours' orientation on the geography of the city, is it any wonder that crews get lost on the way?

It is said -- not by Mayor Barry but by senior advisers -- that the mayor isn't inclined to replace Chief Coleman anytime soon. The reasons, they say, are a combination of personal, racial and political considerations. Mr. Barry is said to believe that the problems of the department are longstanding and transcend the management of Chief Coleman. The mayor also has told advisers that he does not want to force the chief to retire because the departure of Mr. Coleman, who is black, would be seen as a victory for the firefighters' union, whose most vocal leaders have been white. The mayor believes as well that this also might generate protests from black voters. In addition, city officials say Mr. Barry agreed last year to let Chief Coleman stay through August of this year, when he would be the first black fire chief to preside over a meeting in Washington of the International Association of Fire Chiefs.

But who are the principal victims of poor ambulance service in this city, if not black people? And with black as well as white candidates to succeed Mr. Coleman, what is the mayor proving by not doing what should be done? Above all, if anybody else had a record as poor as this one, would the public say "never mind"? Who is fooling whom here, anyway? The people of this city, black and white, demand and deserve the best emergency services possible. The current chief has had many chances to improve things -- and has failed. Mayor Barry should stop trying to paper over this failure and act as he would, and should, in any other emergency of this kind.