Most companies are in the business of charging for services, so the answer is more than likely no. However, there are a lot of people out there who are always interested in free firewood!
Here are your two options:
1. Contact a custom sawmill operator to determine if they are interested in your logs. You will need to know the tree species, diameter, and merchantable log length; and they'll likely ask you to take some pictures to determine if its worth their time and effort.
IL Custom Sawmill Operators: http://www.illinoisurbanwood.org/documents/ILCustomSawmillsDirectory2011.pdf
2. Put an advertisement in your local newspaper (online and print versions) indicating free wood for the taking -- first-come, first-served!