The 49-year-old former Northwest Airlines boss, an ambitious political neophyte with a self-made fortune worth $700m (pounds 425m) and rising, has spent more money, faster, than anyone in a single state race in American history. In a state where voters traditionally rely heavily on candidates' advertisements to make their choices, 60 per cent of people say they have seen "a lot" of Checchi ads. The polls turned up a surprise this month, however. Lieutenant Governor Gray Davis, a figure of neither wealth nor glamour, who has served in a succession of worthy but minor political offices, took the lead.
"Dull wins," says Mr Davis, who sells himself as a "tried and true" elected official, and relies on traditional Democratic allies such as unions and teachers. He was the apparent beneficiary of a string of attack ads unleashed by the Checchi camp on the third Democrat and only woman in the race, Congresswoman Jane Harman.
Mr Checchi, Ms Harman and Mr Davis square off this week in the first and only debate of the campaign, less than a month before the 2 June primary vote. They will be joined by the dominant Republican, California's Attorney General, Dan Lungren, a staunchly conservative former aide to Richard Nixon best known for his run-ins with California's marijuana clubs.
The curious format reflects California's new "open primary" system. Each party chooses one candidate for the general election in November. But in the primaries voters do not have to stick to their own party - Republicans may cast their vote for their favourite Democrat, and vice versa. Mr Checchi, as a businessman, stands to gain most from Republican "crossover" voting.
California is enjoying the good times, and issues are hard to come by. Crime and unemployment are down, house prices bouncing up. The wind has gone out of the bitter rows over immigration. President Bill Clinton's Teflon approval ratings warn pollsters that even scandal isn't selling. Education in California's long-impoverished state schools is named as the voters' top priority, a less than sexy cause that candidates have all been quick to embrace.
It has only heightened Californians' long-standing lack of interest in conventional politics. Only six per cent say they are following the election "very closely". Local newscasts barely bother with it. Los Angeles television stations recently cut live from children's cartoons to an afternoon freeway stand-off in which a man shot himself, as helicopter news crews circled above. But they do not plan to interrupt regular programming for the campaign debate.
As a result, the candidates have been slogging it out in their one guaranteed avenue to voters - television ads. The tone has been thoroughly negative. One recent Checchi attack ad accused Mr Davis on slender grounds of blatant "trading cash for favours", taking half a million dollars from "Wall Street and bond lawyers" in return for directing state pension investments their way. The Davis camp fired back, accusing Mr Checchi of firing 4,000 people in his tenure at Northwest and calling him "a man who killed kindergarten legislation to save a tax break for his airline".
Mr Checchi's vast wealth - his stock has gained $120m in value since he joined the race last autumn - has given him a huge leg up in his bid to be California's Ross Perot. The Democratic election has become "a thumbs up or a thumbs down on Checchi", said a California pollster, Mark DiCamillo. "The race will probably turn on Checchi." But the question is why he is not doing better. In the last two months, his support has topped out at 17 per cent, compared to 19 per cent for Mr Daviswho has no private resources, and has budgeted only $6m on advertising. His aides say the "lies and exaggerations" in Mr Checchi's ads have backfired.
But Barbara O'Connor, a campaign advertising expert, has a slightly different explanation. In her home city of Sacramento, the state capital, she says advertising is so heavy that "you cannot watch nightly television without getting 20 or 30 spots in three hours. There's so much of it, and the clutter is so great, that people are just tired of it. My guess is they are walking out of the room, changing channels, or muting."