65 ILCS 5/11-13-5
In municipalities of less than 500,000 population, the regulations authorized by this Division 13 may provide that the board of appeals or corporate authorities may determine and vary their application in harmony with their general purpose and intent and in accordance with general or specific rules therein contained in cases where there are practical difficulties or particular hardship in the way of carrying out the strict letter of any of those regulations relating to the use, construction, or alteration of buildings or structures or the use of land. If the authority to determine and approve variations is vested in the board of appeals it shall be exercised in accordance with the conditions prescribed in Section 11-13-4, subject to the power of the corporate authorities to prohibit, in whole or in part, the granting of variations in respect to the classification, regulation and restriction of the location of trades and industries and the location of buildings designed for specified industrial, business, residential and other uses. If the power to determine and approve variations is reserved to the corporate authorities, it shall be exercised only by the adoption of ordinances. However, no such variation shall be made by the corporate authorities as specified without a hearing before the board of appeals.
65 ILCS 5/11-13-5