http://www.clickdesk.com/ < is my favorite live chat suite. there is even a free version you can probably get away with using. lots of features like pro-active chat, chat from skype or gtalk, send a call to their phone, ect
We think very highly of Twitter Boostrap at ClickDesk. We recently redesigned our entire website with Bootstrap.
Check out our website - http://www.clickdesk.com/
We also blogged about why we love Twitter Bootstrap - http://blog.clickdesk.com/why-did-clickdesk-choose-twitter-bootstrap/
ClickDesk ( http://www.clickdesk.com/ )
Beyond just live chat, offering multi-channel communications (chat, phone, helpdesk, social) at an affordable price to Startups and SMBs.
Of course, would love feedback.
Check out ClickDesk (http://www.clickdesk.com/)
We solve the problem you've mentioned by the use of departments. You can designate a group of users to a department and have them receive chats originating from a specific page/website. You can add any number of departments.