The answer is likely no. The general rule in Illinois is that an "at-will" employee (meaning an employee that is not under contract with his employer for a specific amount of time) can be terminated at will with or without cause. The same holds true for an employee if he or she wishes to quit at any time. Therefore, an employer may terminate an employee for any reason unless (1) it violates public policy or (2) the intentions of the employer are unconstitutionally discriminatory under state or federal law.
Discriminatory discharge as a claim against a former employer requires proof that the discharge was a direct result of some sort of public policy issue. In Illinois, this means (1) the employee was fired because he or she filed a workers' compensation claim or (2) the employee was fired because he or she turned the employer in for some type of federal or state regulatory crime.
Unfortunately, your facts do not seem to indiate a good wrongful discharge case could be raised. If you have substantive questions I would recommend a second opinion by contacting the Illinois State Bar Association lawyer referral service at (217) 525-5297. Ask them for an employment attorney in Cook County. I doubt there are many, but Chicago is the most likely place to find them.
NOTE: This answer is not intended to be legal advice and should not be construed in that way. This answer does not create an attorney-client relationship and no such relationship may be created absent a signed retainer agreement. The author is licensed in Illinois only, and his answer is for educational purposes alone.