So there was a long discussion thread here about other chat systems such as Comet Chat, Arrow Chat, and some others that you can install yourself.
https://vborg.vbsupport.ru/showthread.php?t=176924
The Envolve chat is hosted because we can provide better service for large sites this way (apache + php doesn't do real-time stuff very well), and because this way we can update everyone immediately when we fix bugs / add features / etc. Did you try it out? Any feedback other than the hosting issue? Why is us hosting the service a negative for you?