To the array of problems he faced in trying to break Illinois' no-third-term tradition in a year when double-digit unemployment has hit this and other cities, Gov. James R. Thompson (R) now must add the "Kikuchi credibility crisis."

The governor went into the first campaign debate here Monday with firm advice from his wife and staff to present a positive picture of his six-year record but not, as one adviser said, to "nit-pick away" at his Democratic opponent, former senator Adlai E. Stevenson III.

But when Stevenson used his opening statement to paint a dreary picture of bankruptcies, business failures and unemployment engulfing the state, Thompson tossed aside his prepared remarks and went right after his challenger.

It is "offensive" he said, that Stevenson would repeat statistics "he knows are untrue. . . . I never said an untrue thing to get to be governor, or to stay governor. I think more of the office than that."

As a former prosecutor, Thompson more than held his own in the exchanges with his soft-voiced rival. But on one critical point it was Thompson who backed down, and today that fact was dominating the post-mortems by politicians from Springfield to Chicago.

In response to a question about foreign investment Thompson cited the trade missions he had led to Japan and other countries. Stevenson said that when he was in Tokyo in 1981 his Japanese driver, whose name is Kikuchi, told him he had taken Thompson around the city on an earlier visit.

"I asked him where he took the governor," Stevenson said. "And he replied, 'I took him to antique stores.' "

A wave of laughter and gasps went through the crowd. Thompson had been embarrassed earlier this year by a series of stories about antiques and other gifts he had accepted from political supporters and people doing business with the state.

He immediately replied, "My driver in Japan, Mr. Stevenson, was a state trooper from Illinois, so I doubt very much that you met him."

Within an hour, however, Thompson had confirmed that he also used a car and driver made available by the Continental Illinois National Bank's Tokyo office, which extended the same courtesy to Stevenson on his later visit.

And, Thompson conceded, he had visited an antique store. "But it was a block from the hotel, and I walked."

The exchange, which was featured in the television coverage of the debate and discussed on radio talk shows Monday night, illustrated the difficulty Thompson has had in staying off the defensive in this race.

A tough, aggressive campaigner in his first two elections, he counted on those qualities to overcome Stevenson, who has a reputation as a bland, introverted, moody and enigmatic political figure.

But Stevenson has turned into a semi-tiger in the fight for this office, which his father held for four years, and which he says he coveted before he ever went off to Washington.

While professing disappointment that the debate had turned into a test of credibility, rather than a discussion of the "Stevenson strategy" for economic revival in Illinois, the challenger seemed quite willing to let things go their way.

"Mr. Thompson was on a pedestal for a long time" he said in an interview in his Chicago law office this morning, "but he's fallen a long, long way." He promised "more revelations" of what he called "the imperial governorship."

For his part, Thompson said he thought he had raised an important issue when he reminded people that Stevenson had quit the Senate in 1980 after 10 years, saying he was "bored, frustrated and couldn't get anything done."

He said the issue was whether voters wanted as governor a man who "really is a patrician, a squire, who really isn't comfortable with people. His father," Thompson added, "didn't have the same fear of, and disdain for, people this guy has."

But talking to a reporter over lunch in a Chicago restaurant, Thompson ruefully admitted that "I got suckered by one cheap-shot thing, right off the wall. I got mad, which I'd promised myself I wouldn't do. I confused the arrangements on my two trips to Tokyo. And I gave an answer to a really BS thing that put the story in the papers."

The personal tone of the debate and the post-debate interviews add a tinge of bitterness to what was already one of the year's key political races. Thompson is one of the only three Republican governors seeking reelection in the Midwest, after five others bowed out. Stevenson has made it clear that he is interested in the presidency if he succeeds in Illinois.

Despite the recession and a year of media attacks on his use or abuse of official perquisites, Republicans say their polls show that Thompson is not more than 4 to 6 points down. And he has some resources Stevenson cannot match.

He has raised $4 million, has $1 million in the bank and expects to raise another $1 million in the next two months, for a massive media blitz. By contrast, Stevenson has raised just over $1 million, and last week made a personal loan of $50,000 to the campaign to get some TV spots produced.

Whether they get on the air is problematical. Despite a surprise endorsement from the state AFL-CIO, union contributions have been negligible so far. The Chicago Democratic organization has made only a token gift. Jewish contributors are holding back.

Stevenson and his aides attribute the problems to his "independence," his refusal to back off his criticism of some labor "featherbedding" practices and his belief that Israel "must make some sacrifices" to permit a solution to the Palestinian problem.

But Thompson said that in every case the cause is deeper. "Labor people, regular Democrats, Jews, they sense he really doesn't like them," Thompson said. "When people have problems, they don't want a governor who puts himself behind a wall of indifference."