Creates the Legal Deserts Act. Provides that, subject to appropriation, the Administrative Office of the Illinois Courts may establish a program to provide grants or reimbursements to compensate an individual lawyer or law firms that relocate or open an office within a geographic area for the purpose of providing legal services to individuals residing within a legal desert. Provides that the grants or reimbursements may cover marketing expenses, compensation for an attorney or up to 2 attorneys per firm, or other eligible expenses identified by the Administrative Office of the Illinois Courts.