I was recently trying to set up Personalized Content on a page in our CMS using Chrome. I successfully created 3 Visitor Groups...but when I went to edit the web page the Personalized Content would be on, after clicking the Personalize Content (green) button, and then clicking the plus sign to select a Visitor Group, the lookup list did not populate with my three groups. The entire popup box appears to be buggy - clicking Cancel or the X doesn't close the window either. I am using Chrome Version 28.0.1500.95 m and its up to date.
This was the first time I attempted to set up Personalized Content so I thought I was doing something wrong. But I went to Internet Explorer and tried there and it worked fine - the lookup list populated with my three Visitor Groups and I was able to set it up.
Once I saved the page in Internet Explorer, I went back to Chrome to see if the Personalized Content showed up - and it did. But I still cannot change or access Visitor Groups in Chrome when setting up Personalized Content.
Your post doesn't say which EPiServer version you were using, but considering Visitor Groups weren't introduced until 6 R2, and it seems to work fine in 7.0, I'm assuming it's 6.1.379.x.
I was able to reproduce this bug in Chrome on a live site using CMS 6.1.379.502. Visitor Group lookup while editing works fine on IE but not Chrome.
File a bug report if you haven't already found a workaround (please share if you did).
I am facing the same issue with EPiServer 6.2.267.1. Has it been fixed?