Washington area residents are sharply divided over the question of federal aid to the ailing Chrysler Corp., according to a recent public opinion sampling.

Of 300 persons questioned in a random telephone survey conducted by Southeastern Institute of Research Inc. of Richmond, 43 percent opposed U.S. financial support for Chrysler while 38 percent were in favor and almost 19 percent were undecided.

Because the number of opponents and supporters of Chrysler aid were so close, the margin for error in such sampling indicates that the respondents with opinions were about evenly divded -- while about one-fifth had no view.

But the survey did show a significant difference of opinion among Washington area men and women. By a 50.7 percent-to-36 percent margin, men favored aid to Chrysler while women opposed such assistance by a 51 percent-to-25.5 percent margin.

Moreover, 53.5 percent of all black respondents to the survey supported federal financial assistance to Chrysler, which has one of the largest minority work forces in American industry.

Supporters of the Chrysler financial aid said such an investment would save jobs and benefit the whole economy while a failure at the nation's third-largest auto manufacturer would add up to unemployment aid costs higher than the proposed federal aid.

Individuals who oppsed Chrysler aid said the corporation should be able to get enough financial assistance on its own and that aid would set "a bad precedent" and violated free enterprise principles or that it was a "waste of money . . . won't help."

The Southeastern Institute conducts regular marketing and opinion research for national, regional and local clients, including monthly samplings on various issues in the Richmond and Tidewater areas of Virginia as well as metropolitan Washington.

Questions about Chrysler were asked during interviews between Nov. 27 and Nov. 30.