Legal Question in Landlord & Tenant Law in Illinois

Every Chicago lease, whether or not it is subject to the Chicago Residential Landlord & Tenant Ordinance, is supposed to have a summary of the Ordinance attached to it, or somehow incorporated into it. You should become familiar with the Ordinance. Here's a link to it on the Metropolitan Tenants Organization's website:

http://www.tenants-rights.org/residential-landlord-tenant-ordinance/

You will find that rodent infestation constitutes a material failure to maintain (assuming the infestation was not caused by the tenant) and can result in termination. Look in particular at section 5-12-070, and 5-12-110. Whether your building is covered by the Ordinance is Section 5-12-020.

If your building and lease is NOT covered by the Ordinance, Illinois has a similar law called the Residential Tenants' Right to Repair Act, but it does not allow termination -- only the tenant's right to repair within stated limits.

The only other way to deal with this is to risk eviction or a rent lawsuit on the assertion that the conditions make the apartment "uninhabitable" and/or the conditions constitute a "constructive eviction" but those strategies should only be attempted with an attorney's help after defining your goals.