State officials kicked off the private renovation of the building which once served as the state government’s Chicago headquarters.The James R. Thompson Center, as it was known under state ownership, was sold in 2022 to a development firm that is renovating the building for its to-be occupant, Google. In exchange for the building, the state received $30 million and a $75 million office building on LaSalle Street in Chicago.The Silicon Valley-based tech giant intends to use the building for its Chicago offices after …