Creates the Expanding Medical Residency Opportunities in Illinois Act. Provides that the Department of Public Health shall establish a grant program to provide funding for medical residency positions not funded by certain federal or other funding sources and to provide startup funding for entities that wish to establish a residency program. Provides for procedures, criteria, and other requirements for the grant program. Creates the Medical Residency Fund as a special fund in the State treasury. Defines terms. Makes conforming changes to the State Finance Act.