Chrome cannot run GMail

This is terrific. A few years ago, Google launched GMail to knock Hotmail and similar services off of the top of the freebie email heap. A couple months ago, they launched Chrome-- the Google spawned web browser. GMail has chat functions. After some recent tinkering, the chat functions do not work in Firefox. They also do not work with Google Chrome. How could the GMail people not do compatibility testing on their company's web browser? They don't even recognize or support Chrome.