Google initially supported chat with its client software, Google Talk. Then, it integrated chat right into the Gmail interface, allowing users to chat from any browser, without having to install software.
The official Google Chrome extension, Chat for Google, now lets you conveniently have chat windows outside of your browser. You can even start Google+ hangouts from it.
After installing the extension from the Chrome Web Store, right-click on the browser button to configure its options.
If you're restricted from installing software on your computer (maybe at the office) or you prefer not to use the Google Talk client, the Chrome extension is a nice alternative. Keep in mind, however, that the extension does not currently support Google Voice calls or file transfers.