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I'm afraid not. Paintchat requires you to install Java software on your server and run it under your shell account, and only limited numbers of servers will allow you to do that. Very few people would be able to get it working.
It also suffers from the same technical problems as PaintBBS and ShiPainter, which means that Paintchat will likely not work properly with most web browsers by the end of this year (Java no longer works in Chrome, and support will soon be axed for Firefox).