Washington — Warren Burger, chief justice of the United States, was plainly exasperated. He leaned forward in his chair, brushed back a shock of white hair, and addressed the defense attorney who was facing his court: ''This raises a significant question of social costs in a case that has gone on for 15 years . . . handled by 35 judges . . . (and where) there's been no question about guilt.''
Then the chief justice asked the lawyer why ''a plainly guilty defendant should go free for a grisly murder?''
Justice Burger, in his comments on this case involving the so-called exclusionary rule, was expressing not only his own point of view but the frustrations of many other Americans. They regard this rule as overly protective of the guilty while victimizing of the innocent.
The exclusionary rule, a 70-year-old standard in criminal law, bans evidence and confessions from court if they have been gathered through improper police procedures. The rule is being challenged by the Reagan White House, the Department of Justice, and most law enforcement agencies across the United States.
Recommended as an alternative is a ''good faith'' exception, which would admit evidence if it could be shown that police acted honestly, though mistakenly, in searches, arrests, or questioning.
The case before the Supreme Court involved a suspect in the murder of a young girl. While the suspect was en route to turn himself over to authorities, a police detective informally urged him to reveal the location of the victim's body. The detective delivered what is now known in legal annals as the ''Christian burial'' speech: ''The parents of this little girl should be entitled to (give her) a Christian burial,'' he said. It was those words which, after the accused was convicted and sentenced to life imprisonment, triggered a decade and a half of appeals. The case was before the Supreme Court for the second time.
No longer at issue was the defendant's guilt or innocence - but his constitutional rights: first, to counsel at the time of his arrest, and now the question of whether he was improperly pressured into revealing the victim's whereabouts, which he did, after the Christian-burial speech.
This case is more dramatic than most exclusionary-rule controversies. Those who advocate change, however, use it to make their point: The law tilts toward the guilty and hinders the cause of justice by encouraging lengthy and costly appeals on technical grounds.
The rule's defenders insist it is used sparingly and seldom prevents prosecution. (One study shows that only 2.3 percent of drug arrests are not prosecuted be-cause of procedural problems. Another shows the figure to be even smaller in other criminal cases.) Supporters of the rule also say it provides a necessary bulwark for the Fourth Amendment, which guarantees defendants a fair trial and forbids unreasonable searches and seizures and other police abuses.
Who is right? The court will rule later this year. Yet a decision either way seems unlikely to solve the problem fully. If the court upholds the rule, some defendants will continue to abuse the system. If it modifies the rule or abandons it, others - primarily law enforcement people and overzealous judges - may be tempted at times to ignore the Fourth Amendment.
No matter which way it goes, there are several lessons here. First, the arrest system needs shoring up. And one way of minimizing error is to sensitize law officers to the constitutional rights of the accused. Judges and local magistrates also need to be better schooled in this area. (Reportedly, there are over 10,000 magistrates in the US who are not even law school graduates.)
But the exclusionary-rule controversy also points up a need for new approaches to criminal justice. In the area of incarceration, the chief justice and others are already outspoken about changing overcrowded prisons from inmate ''warehouses'' to institutions in which schooling and job training point a way to useful careers. This approach is to be appauded.
But why can't the same kind of creative thinking be applied before lockup? One way to start would be for the advocates of tougher tactics and harsher punishment to agree with the proponents of fewer restraints for the accused, so as to take the matter out of the political spotlight.
The jawboning is counterproductive, because it tends to polarize the public. Cooler heads may perceive that the worst fears of both sides are ill-founded. America is not rife with criminality because of the exclusionary rule.
Nor is there any serious danger of the nation's becoming a police state if this concept is modified to shore up the effectiveness of certain police procedures. There are other ways to protect society against police excesses.
If we're really serious about ''good faith,'' let's focus on making the system work more efficiently though innovative methods, enlightened law enforcement, and cost-efficient administration of justice. Then we'll all be better off.