The Illinois Schedule 1299-I Income Tax Credits Information and Worksheets has this definition of basis:
"Generally, the basis will be the purchase price, plus any capital expenditures, minus any rebates and IRC Section 179 deductions. The basis is not reduced by depreciation, including bonus depreciation, except depreciation you were allowed to claim before the date you placed it in service in Illinois, or in an Illinois enterprise or river edge redevelopment zone."
In other words, Illinois is asking "how much do you have invested in this property, net of any rebates or Section 179 deductions?".