To add ShoutBox in Wordpress, you should go to Widgets section of your Blog.
You can find widgets on Appearance – Themes section of your dashboard.
At widgets you can find an option to add HTML / Text. Select that option and you will get a textbox to enter the shoutbox / chatbox html code.
After entering code, save that widget. Now you can find the shoutbox displayed at the sidebar of your Blog / Website.