I agree with mjuergens but if possible, it would be worth testing on an external monitor to ensure that this is actually the case.

In the case that the line appears on the external monitor it could be a graphics chip issue which would mean a logicboard replacement or maybe a graphics chip "reflow".

If not then you can replace just the LCD as per instructions on iFixit and source your LCD from the store or from somewhere like eBay.

TIP: When mounting the LCD into the macbook top lid ensure you wear latex gloves.