You can own a bali in Illinois, not sure about Chicago specifically though. However, Chicago has a city ordinance that bans carry of knives of 2.5" blade length, so that knife is definitely not legal to carry in the city.
With all the crime in Chicago, police likely aren't going to be too focused on measuring knife blades on people they contact. That said, carrying a bali in general is pretty much asking to get arrested for carrying a "category 2 weapon" under the provision covering "any other weapon"...I don't think any knife screams "criminal" more than a bali does and there is really no legitimate reason for someone to carry one.
In summary, definitely not legal to open carry and definitely not smart/probably going to get you arrested for carrying at all in Chicago at least.