FORTUNE -- When Newt Gingrich and his Republican revolutionaries seized control of Congress last fall, delight in many corner offices that Washington might finally move to cut federal spending and roll back noxious regulations was dampened by doubts about whether the new Speaker was up to his responsibilities. Indeed, for most of Gingrich's career, his relations with the men who run America's largest corporations have generally ranged from distant to frosty. To him, the big-business crowd, while sympathetic to his aims, have been too stodgy, too timid, too compromise-prone, and--worst of all--too willing to donate PAC money to the powerful Democratic barons on Capitol Hill. To them, Gingrich has been an intriguing but unnerving upstart: too radical, too quick to shoot from the lip, too self-consciously intellectual--in short, just too weird. So where do things stand now? Fortune's latest exclusive poll of the heads of America's largest corporations provides the answer: Nine months into the new regime, big business finds itself living happily--though still warily--with Newt. In an August survey of Fortune 1,000 CEOs conducted by the opinion research firm of Clark Martire & Bartolomeo, 93% of 201 respondents voiced approval of Gingrich's performance as Speaker. Most striking, 49% of top executives rose up on their wingtips and said they "approved strongly." By contrast, just 31% of voters--and only 53% of Republicans--in a recent CNN/USA Today Gallup poll held a "favorable" opinion of Gingrich. Insists Kenneth Duberstein, who served as chief of staff in the Reagan White House and now advises a number of major companies: "Corporate America has gone ga-ga over Newt."