@Wonderful Togbey Wonderful, congrats and welcome to Chicago, the home of "The Professional Renter."
Tenants in Chi are notorious for using the law against their landlord to stay in their apartment without paying for any reason and can end up staying for sometimes up to a year without paying. If you evict in Chicago in NORMAL conditions it could be 6 months. With coronavirus, who knows how long it would take to evict. I agree with Bree and John above. If it were me, I'd go to a month-to-month with Bree's language, and take a move-in fee on new tenants. Last resort - if they stop paying you may have to implement, "Cash-for-keys" - an expedited way to get them to move out without waiting for cook county sheriff to arrive/courts to open 6-12 months - GIVE THEM MONEY for a moving truck. I know this is counter-intuitive, but its the only thing that worked in the last recession because the tenants are smart in Chi (again, last resort). Better to keep amenable if possible.
It's possible the previous landlord took a non-refundable move-in fee instead of a security deposit, which could be why you don't have one.
As for security deposits, in any other market I'd say that's fine. In Chicago, you have to pay interest on their security deposit and if you mess that up in any way, they can sue you, some have even gotten an entire year of rent in damages from their landlord by being off $0.02 (I wish this was just a joke). So as a result, most landlords have shifted to the non-refundable move-in fee. If they damage the apartment you would need to pursue them ANYWAY with a security deposit (if the damage is more than the deposit), so same goes here, you'd still need to pursue them. In fact, some of my clients with 1,000s of units only use move-in fees because they get to keep it and not return on move-out and it gives another line-item of income...