Support

I do not have any recommendations. Chat is something I neither use nor recommend as a user engagement option.

As a client, I vehemently hate chat. It combines the worst attributes of calling on the telephone (it has to happen in real-time) and ticket-based support (you need to wait a long time between replies), with the added complication that the agent does not have the time to read through the chat or my client record to understand what I am saying. What could've been 5' exchanging two brief emails expands to an hour of me mostly being idle, staring at the screen, waiting for a reply, while getting increasingly frustrated.

If you (or, rather, management) want to unleash the infernal horror of chat upon your unsuspecting clients then sure, there are plenty of chat solutions for Joomla. Just keep in mind that some of them use an arbitrary .php file as a directly web accessible endpoint which means you'll have to add it as an exception in Admin Tools' .htaccess Maker. Ask the chat software developer which, if any, .php files need to be directly accessible over the web.