We've asked Apple for comment on the issue. It doesn't appear that restarts or other common software solutions fix it, though, and this might be strictly a hardware problem. It's not necessarily an overscan line like you might see on a TV, either. No matter what, it's safe to say that you can get a replacement if the usual troubleshooting proves fruitless.
It's unclear how many people are affected by the green line, although it doesn't appear to be a widespread issue. Between this and the (software-fixable) cold weather responsiveness issue, though, it appears that the iPhone X has some teething troubles. That's not entirely surprising. It's Apple's first phone to use an OLED screen, and it's using a custom (Samsung-manufactured) panel at that -- there may be a learning curve involved as the companies master their production techniques. As it is, Samsung has had problems with its own OLED phones. Provided the iPhone X flaw is a hardware issue, it illustrates the broader issues with manufacturing cutting edge OLED screens.