That’s an easy answer: p52 (a fragment of John 18). Perhaps not. P52 is typically dated to A.D. 125-175. There is a fragment of Matthew 21, p104, that is dated to A.D. 100-200. The mean age of both manuscripts is A.D. 150, but if p104 is as early as its terminus a quo, then p104 may be the earliest NT manuscript.
Of course, there is still the possibility that we have a fragment of Mark’s gospel dated to before A.D. 90. The court is still out on this one since the research on this fragment has yet to be published. If it turns out to be a valid date, it would be the first NT fragment from the first century to be discovered – an exciting prospect indeed!