Horizontal line?
You could try hooking up that monitor to something else (iirc you have a LCD monitor right?) to check if it's a flaw in the monitor or try different cables (VGA, DVI or HDMI if you have the output and input for it on Graphics card and Monitor)
Analog cable:
VGA
Digital Cable:
DVI:
HDMI:
When I got thise new system I noticed faint horizontal lines whenever I played a game this was because my PSU on the bottom of the case close to my Graphic card's output and when the PSU was working at higher capacity it caused to screw around with my analog signal causing black faint lines across the screen. I solved it from going from Analog (VGA cable) to Digital (HDMI).
So if you have DVI or HDMI cables lying around and you have the output for it on the graphics card and the input on the monitor give it a go.
HunterICX