At the risk of being the bad-news messenger, the answer is that nobody has a legal right to a job, and employers are required to constantly make choices. No law prohibits an employer from choosing to not hire someone with a criminal record.
This answer is offered as a public service for general information only and may not be relied upon as legal advice.
As you're in Illinois the Illinois Human Rights Act governs your situation and depending on the specific facts what you're describing may be a violation of the law. But it is case specific so I would give an attorney a call on Monday to see if your situation fits.
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An employer can hire or fire for any reason, no reason or even a wrong reason. Illinois is an at will employment state. Unless you are a union member or were discriminated against because of your membership in a protected class such as race, religion, etc., you are probably out of luck. Conviction of a crime is not a protected class so you were not discriminated against. Unfortunately, you are limited to seeking employment where background checks are not conducted. Sorry.
There are certain restrictions on using criminal history to deny someone a job. However, your crime based on the punishment does not appear to be one of them. You should contract the IDHR and talk to them.