Synopsis As Introduced Creates the Build Illinois Homes Tax Credit Act. Provides that the Illinois Housing Development Authority and the City of Chicago Department of Housing may award credits for certain qualified low-income housing projects. Provides that the credits may be taken against any or all of the following: (i) the taxes imposed by the Illinois Income Tax Act; or (ii) any retaliatory or privilege tax imposed by the Illinois Insurance Code. Amends the Illinois Income Tax Act and the Illinois Insurance Code to make conforming changes. Effective immediately.