What is your latency between the two sites? Anything over about 120ms latency is going to play havoc with your voice, especially if there is a lot of jitter. Meaning the response times vary more than just +/- a few ms from packet to packet.
Are the calls coming into the 3cx system via a voip provider?
You would have better luck with a 3cx system on the europe side with a bridge between the two systems. Then you can setup either a voip provider or some other form of dial tone for your europe location so calls are not going back and forth the whole time. I am betting the latency from chicago to europe is rather high.
Is there a VPN between the two locations? If there is a vpn you could reduce some overhead and send the calls directly across to Chicago, going around the VPN to test.
If you haven't already you should put in place firewalls that will allow you to prioritize the voice traffic, once its on the net you loose control of course but at least you can give it a fighting chance.
A dedicated circuit between locations would be your best bet for lower jitter/latency but at a high cost.