LCD line of dim pixels

I just got a new LCD monitor. There is a small horizontal line on the
screen. It is about 2 pixels high and 100 pixels wide.

The pixels don't seem to be dead, they are just not as bright as their
neighbors. I tried moving a window with a red, green and then blue
background and the line appeared for all 3 squares.

Is this kind of thing normal for an LCD? I read elsewhere that
sometimes dim pixels fix themselves. If I leave the screen on for a
while with a white background might the problem go away ?