Raz for Chief Justice

This post may eventually become answers to questions only I was wondering about, part IV. While reading a post at Volokh Conspiracy on dark horse Supreme Court nominees, the name Joseph Raz popped into my head. But Raz isn't a U.S. citizen. I thought this would be the end of it, but I couldn't remember ever having seen a source for a rule preventing non-Citizens from becoming Judges. To be on the safe side, I checked. The Constitution, while imposing citizenship requirements for the House, Senate, and Presidency, is silent on the matter for Judges. I looked in both Article III and the appointments clause, and I can't think of where else such a requirement would be found. I must be missing something obvious, but if this requirement isn't in the Constitution, it seems to me there is no such requirement. I'm fairly certain any statute on point would be an unconstitutional violation of the Appointments clause, and the same would have to apply to case law, I think. Any thoughts would be greatly appreciated, though I expect to be embarrassed when I hear the answer.

Update: I should note that I know essentially nothing about Joseph Raz, and as such have no opinion on his qualifications for any judgeship, or complete lack thereof. I just think this foreign citizen issue is very odd. Also, I'm quite anxious to hear an answer, though not quite enough so to do real research.