An article on Saturday about the variety of fashion choices made by New York City's judges misstated the title once held by two former United States Supreme Court justices — John Jay, who was often pictured wearing a scarlet and black robe with silver trim, and John Marshall, who departed from tradition by wearing a plain silk black robe. They were chief justices of the United States — there is no such title as chief justice of the Supreme Court.
It's true that the U.S. Code almost exclusively (with one minor exception) labels the Chief Justice as "the Chief Justice of the United States." But in fact he is also the chief justice of the Supreme Court — there is a Supreme Court, there are justices of it, and he is the chief justice among them. (Note that the original article spoke of "the chief justice of the Supreme Court," with "chief justice" in lower case. That suggests the article was describing the office, and not giving an official title; if it were capitalized, that might be more ambiguous as to whether it's a description or a title, though even there it could be read as a description.) So whatever the official title may be, "chief justice of the Supreme Court" is a perfectly proper locution.
But this isn't just my view. It's also George Washington's, speaking to John Jay himself when Jay was first appointed: "Sir, It is with singular pleasure, that I address you as Chief Justice of the Supreme Court of the United States, for which office your commission is enclosed." ("Chief Justice of the Supreme Court" would be a naturally abbreviation for that.) It's also Hamilton's or Jay's in Federalist No. 65, which spoke of the proposed Constitution's "making the chief justice of the Supreme Court the president of the court of impeachments."
It's St. George Tucker's view in his Appendix to his highly influential 1803 edition of the Blackstone's Commentaries (in turn quoted by Chief Justice Joseph Story in his highly influential 1833 Commentaries on the Constitution), where Tucker spoke of how "the constitution expressly requires that the chief justice of the supreme court shall preside" at an impeachment trial. It's the view of the Congress that enacted the Judiciary Act of 1802, which spoke of "the present chief justice of the supreme court" (who at the time was Chief Justice Marshall). It's the view at least at times of Chief Justice Marshall himself, who signed some documents, "Witness the honorable John Marshall, chief justice of said supreme court." And these are just early examples; there are lots more from later decades.
So if you want to tell all these people that their usage was invalid, or is no longer valid because of what intervening Congresses have done, be my guest. (You can't tell them that their usage is no longer valid because actual usage has changed, since in today's actual usage "chief justice of the Supreme Court" is quite common, and in fact a little more common than "chief justice of the United States," as either a Google search or a Nexis search will confirm.) But I can't see why the rest of us should be persuaded of this, and should reject the judgment both of modern usage and of historical usage (buttressed by the normal presumptions of English phrase formation). This latter judgment, I think, is that both "chief justice of the Supreme Court" and "chief justice of the United States" are perfectly correct.