If your building is in Chicago and is covered by the Chicago Residential Landlord Tenant Ordinance (CRLTO), then this situation is specifically addressed in Section 5-12-110.
This section states that if there is an infestation you may deliver a 14 day notice to the landlord, giving him that time to correct the problem. If the problem is not then corrected, you will be able to legally break the lease.
I don't recommend doing this on your own. It is important to get the assistance of an attorney who handles landlord tenant issues to properly deliver the notice and help you break the lease.
This answer is intended as informational only, and does not constitute legal advice or form an attorney-client relationship between us.
You may have a basis for breaking your lease but you should consult with an attorney who handles landlord problems. You might be able to locate some online help, but there is no substitution for an in-person discussion. Special laws apply to Chicago landlords and leases.
One good resource for Chicago tenants who are eligible is the Lawyer's Committee for Better Housing. There are other resources as well that may help you in your efforts to break your lease or negotiate an early termination of the lease, or obtain alternative housing.
As has been stated, Chicago has a strong ordinance protecting tenant's rights.
See the link below:
The information provided here should not be construed to be formal legal advice. The provision of this general advice does not create a lawyer-client relationship. Persons with legal questions are encouraged to seek independent counsel for advice regarding their individual legal issues.