A second threat has been made against the life of U.S. District Court Judge Barrington D. Parker, the judge assigned to preside over the trial starting Tuesday of three Cuban exiles charged in connection with the 1976 bombing death of former Chilean ambassador Orlando Letelier.

In the latest development, Parker received an unsigned, thped letter at his home on Dec. 19 containing threats that the letter writer said he had overheard being made by one of the defendants in the case, according to a government legal brief. The defendants are Ignacio Novo Sampol, Guillerme Novo Sampol and Alvin Ross Diaz, three leaders of the Cuban Nationalist Movement.

Lawyers for the defendants previously asked Parker whether he felt he could preside fairly after it was disclosed that threats had been made Aug. 17 against him and a prosecutor in the case, Assistant U.S. Attorney Eugene M. Propper.

After the first threat was made, Parker said he felt he could handle the case fairly. He denied a defense motion on Dec. 20 in his chambers to step down from the case because of the two threats. Parker yesterday ordered the jury sequestered in the Letelier case.

Security has been increased at courthouse entrances in the wake of the threats and the shooting two weeks ago of Assistant U.S. Arrotney Barry L. Leibowitz in the courthouse parking lot. No arrests have been made in the shooting.