The answer is unfortunately "it depends." Illinois landlord-tenant law is controlled by state law and local ordinances, such as the Chicago Landlord-Tenant Ordinance ("RLTO"). Additionally a major source of legal rights and duties of both landlord and tenant comes from the written lease, which is interpreted by contract law principles.
Here, Illinois state law and the RLTO provides a duty to certain landlords (depending on the size and structure of the building the apartment was located in) to repay security deposits within a short amount of time. Additionally, the landlord is required in Chicago to provide a written receipt upon accepting a security deposit or else forfeit the entire amount on demand. As far as who to sue, an attorney will likely have to check the specifics of the lease to see what it provides for.
However, I must caution you regarding the size of the deposit. You likely will want to hire an attorney to represent you in small claims court since you live in Washington state. The filing and process fees in Cook County will be roughly $200 (which you can get back if sucessful) and an attorney will likely charge at least that if not more to draft pleadings and attending court dates (which, in limited circumstances under the RLTO can be recoverable as well). However, the cost of pursuing action is at least if not more than what you are seeking to recover. You should consider whether the risk of litigation (nothing can be guarenteed) is worth the possibility of recovering such a sum.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.