That's extremely odd. I literally copy pasted what you gave me to make my next example linked below, and it's not happening for me there.
I made some changes to the css here, for the text box, not sure if it's good enough, so I encourage you to play with it yourself -
http://jsbin.com/qolixiyopo/1/edit?css,output
What browser are you using? Chrome, Firefox, IE?
EDIT: Actually, WOW, just tested it on my gf's computer, it IS a problem in Firefox, but not in Chrome.
Weird. I hate it when that happens. I don't actually have Firefox to be able to test fixes for it, but the problem is entirely with the css/html rendering.