You should check with the seller to see if they have set up an arrangement with the tenants. I have a buyout in all my leases with my tenants in the event of sale. I can get possession within sixty days by offering my tenants one months rent. Prepared sellers often have a plan to deal with possible possession.
If not, I recommend having the seller attempt to gain possession prior to closing.
Worst case, if it cannot be done and you love the property, you can take rent from the tenant and give it back to them as an incentive to forfeit possession. This has worked well for me.
You will find that usually the seller has thought about the scenario. Eviction and forced possession in Chicago can be tricky. I recommend consulting your real estate attorney to request advice as well.