1) Welcome to the Party!
2) As you are obviously new here, I have some suggestions to help us all help you:
When you post, please post your entire configuration including (but not limited to) your installation method (7.X.X?) and vicidial version with build (VERSION: 2.X-XXXx ... BUILD: #####-####).
This IS a requirement for posting along with reading the stickies (at the top of each forum) and the manager's manual (available on EFLO.net, both free and paid versions)
You should also post: Asterisk version, telephony hardware (model number is helpful here), cluster information if you have one, and whether any other software is installed in the box. If your installation method is "manual/from scratch" you must post your operating system with version (and the .iso version from which you installed your original operating system) plus a link to the installation instructions you used. If your installation is "Hosted" list the site name of the host.
If this is a "Cloud" or "Virtual" server, please note the technology involved along with the version of that techology (ie: VMware Server Version 2.0.2). If it is not, merely stating the Motherboard model # and CPU would be helpful.
Similar to This:
Vicibox X.X from .iso | Vicidial X.X.X-XXX Build XXXXXX-XXXX | Asterisk X.X.X | Single Server | No Digium/Sangoma Hardware | No Extra Software After Installation | Intel DG35EC | Core2Quad Q6600
3) Depending on your version, have a look at:
/chat_customer/customer_chat_code.php
or
/srv/www/htdocs/chat_customer
Once you get the concept that UNlike Vicidial, this is merely a web page. Nothing special about it. That being said ...
Opening your Vicidial server up to General Public is dangerous and prone to attack. You can minimize the risk by putting this site on a different domain name (ie: set it up so that this site is the web root of a different domain name, and the rest of the Vicidial server is NOT available on that domain name). Then visitors to the site won't see "vicidial" folders or functions. In fact, you could also put that site on a different port, and only open that port (rather than 80) to the general public. Or you could put that site on a different server entirely and link it to the Vicidial database which would then only open the Vicidial Database to that other server's requests.
Mostly, you should have a website-savvy person implement this for you, since one of the many features of this chat system is that it can be re-designed to look like almost any other chat system, or personalized to your company. It can even be put directly on the wordpress server. I'm surprised nobody has built a skinnable Vicidial Chat module for WordPress yet.