Former President Donald J. Trump used a dubious accounting maneuver to claim improper tax breaks from his troubled Chicago tower, according to an Internal Revenue Service inquiry uncovered by The New York Times and ProPublica. Losing a yearslong audit battle over the claim could mean a tax bill of more than $100 million.

The 92-story, glass-sheathed skyscraper along the Chicago River is the tallest and, at least for now, the last major construction project by Mr. Trump. Through a combination of cost overruns and the bad luck of opening in the teeth of the Great Recession, it was also a vast money loser.

But when Mr. Trump sought to reap tax benefits from his losses, the I.R.S. has argued, he went too far and in effect wrote off the same…