That looks exactly like the default "check spelling as you type" underline for the OS, so I'm going to guess it's somehow related. Could be a weird glitch in which the underline is popping up in the wrong place (tried restarting the computer to see if that stops it?), or maybe an app misbehaving somehow (do you have anything open and hidden, and/or anything that might be suspect open?
Possibilities could include anything with a text edit field--a web browser, text editor, or something else...