Supervisor asking me to list a co-author who has literally done nothing I am in the final stages of writing a paper to submit at an IEEE conference. I am the primary author, in the sense that I did most of the work and most of the writing. I have three other co-authors who have contributed a significant amount of advice and proofreading (one of whom is my supervisor).

Last week, my supervisor told me I should add person X as a co-author (in addition to myself and my three existing co-authors). I have never met X and they have contributed absolutely nothing. It's not even clear if X has looked at the work we have done!

My response was as follows: "Fine, if X at least looks at section Y to make sure it has no errors, I'll put them as the last author." This has not yet happened, with less than a week to go before the deadline. My supervisor is still insisting that I add X as an author. 

What should I do in this circumstance?
Based on what you have said, this seems to be a clear ethical violation.
I would send an email to your supervisor asking him/her if X has had a chance to look at section Y. This will force them to either state yes or no as to if X participated. Play dumb if you have to.

Hi [Supervisor]
Has X had a chance to look at section Y in the project? As I remember, we discussed adding X as an author as long as X verified the results of section Y. I just want to be sure that I get the right authorship on this paper.
Thanks, Mahkoe

Getting written directions from your supervisor on this will document any unethical behavior that he/she is suggesting you participate in. Your supervisor will have to either directly tell you to add X even though they have not contributed to the paper, or they will be leveraged into conceding that X does not deserve authorship and should not be added.
If your supervisor still insists that X be given credit in spite of doing nothing, you have a few options:

You can seek out the advice of your department chair or graduate coordinator.
You can refuse to put X in as an author and make your supervisor mad with you.
You can comply with your supervisor and chalk it up to yet another predatory, manipulative adviser taking advantage of students.

You decision here depends significantly on how receptive your department is to students and how much you are willing to risk losing if your supervisor tries to retaliate. I am understanding of the fact that you may or may not really have the leverage to directly turn your supervisor down on his/her demands. Such is the life of a student in academia. A small number of professors know you have no clout and routinely take advantage of students in these situations. And sometimes, it is better for your own sanity and career to let X and your supervisor commit ethical violations and publish your paper without further grief.