Go to this page : http://adwords.google.com/support/bin/answer.py?answer=17472 and in the bottom right corner, at the end of the right sidebar it says CHAT WITH A SPECIALIST.
"If you don't see the button, we're not available to chat at that time. However, we're always available via email, so please feel free to send us your questions using the form provided. We'll be happy to answer your questions." so when adword professional is online then only you will see Live chat button.