Set up two new variables:

The highlighted value above should contain the domain of the chat window.

Ref: https://support.google.com/analytics/answer/6164390
Edit the Universal Analytics Page View Tag, under “More Settings > Fields to Set. Here you will add 2 fields:

Under “More Settings > Cross Domain Tracking

Ref: https://support.google.com/analytics/answer/6164469?hl=en
The highlighted portion above should have the domain of the chat window.