I had a support chat on my business website for a long time; the "business goal" I wanted to further was to make it very easy for people to talk to me, ask questions, etc. I helped out a lot of people with very short turnaround times.

I removed it mostly because it takes a lot of effort to maintain a good level of responsiveness on these kind of things unless you have a dedicated support team.

Some of these support chat popups are a bit too in-your-face, but it sure beats hunting down some email address somewhere.