After googling the message I figured out that this happens when you are using Google Chrome as your browser. If you shut down your computer while Chrome it is still open, this message comes up. I couldn't reproduce it on my PC but it does happen consistently on hers now that we know what is causing it.
Apparently, an engineer at Google thought that it would be funny to use Dr. McCoy's words (when talking to Jim Kirk) in this message without considering how many people out there know someone named Jim and who will some day die. Stumbling on this at the wrong time, could be a very shocking experience.
I found this on Youtube. It is a compilation of all Dr. McCoy's death pronouncements from the original Star Trek: He's Dead, Jim.