Building Chips in America Act of 2023 This bill modifies and limits the review of certain semiconductor (i.e., microchip) projects under the National Environmental Policy Act of 1969 (NEPA) and the National Historic Preservation Act (NHPA). Specifically, the bill exempts from NEPA and NHPA specified semiconductor projects that receive financial assistance under the William M. (Mac) Thornberry National Defense Authorization Act for Fiscal Year 2021. Next, the bill allows the Department of Commerce to serve as the lead agency for the review of a semiconductor project that receives such financial assistance but is not exempted from review under NEPA. A single environmental document and joint record of decision must be prepared for a semiconductor project. In completing the environmental review, Commerce may adopt a prior study or decision under certain circumstances. The bill also allows a state to assume the responsibility of an environmental review under NEPA for a semiconductor project. Finally, the bill sets a statute of limitations for certain claims under NEPA.