Renting to folks with pitbulls

[Jen W.]

This is me and my husbands first out to market rental, potential tenant inquires if we allow pit bulls.  We have another tenant that we inherited at purchase of property that has a pit bull and poodle.  Property is a three unit with fenced in yard.  Two questions/concerns:

1. How do you handle large dogs with bad reputations (pit bulls, rottweilers, etc.)? We are advertising the listing as pets allowed and pet rent will be applied (rent tbd).

2. The pit bull from existing tenant can be aggressive but ultimately friendly, the concern is existing tenant's dogs and potential tenant's dog being in the backyard at the same time (I'd have this concern with any two dogs, regardless of breed).  I want to include a rider/addendum in the Lease that states all pets must be on leash when in the backyard and that the yard is not a dog run and we'd post signage that states dogs must be on leash. 

Is there any other concerns/issues I should have? 

For what it is worth, property is in Chicago, IL.