The same thing happened to me with Firefox. If you put the icon on your desktop to the taskbar, it counts as a shortcut, and launches the actual program, and both the shortcut and the actual program stay on the taskbar. Here's how I fixed it:
1- Remove the shortcut from the taskbar while Chrome is open.
2- The shortcut is gone, while the actual thing remains.
3- I don't know what the option is called on the English Windows, but right click the Chrome on the taskbar and attach it to the taskbar.
4- It should work properly now.
