After trying out a number of edits to try to get phpFreeChat to work with WordPress I finally came up with a simple, and somewhat old-school solution.
1.) Setup the chat as you normally would. I used the 'chat' folder for this.
2.) In WordPress use the following HTML code for either a Page or a Post (it works in both)
<iframe src="http://www.yoururlhere.net/chat/index.php" name="Chat" width=640 height=480>
</iframe>
This will embed the chat into the Page/Post. Depending on the theme you use there may be limitations on the space that you can use. In my case I had to remove the date/time, bottom smiley bar and change the height of the chat to about 320px. I have full functionality with this solution including private messaging and creation of new channels (which appears to be a proble with some other solutions I've read about)
I believe this solution will probably work on many (if not all?) other blog websites.