The game doesn't launch for numerous people. That should be investigated. Some say it might have something to do with Visual C++ Redistributable for Visual Studio...
Topic on Talk:Chrono Trigger
I am unaware of the particular details, but it seems having a libEGL.dll in the game folder fixes it. You can either use this one from Next Up Hero: http://cloud.aemony.se/direct/view.php?s=da133361a9f8da61&/libEGL.zip
Or you can even create an entirely empty text file and rename it to libEGL.dll and that will fix it as well, although you'll get an error message on startup of the game before the game window shows up.
Seems the issue is almost certainly caused by one of the latest Windows updates.
Thanks Aemony, you are amazing. How did he figure out this solution?