Since the Chief Justice of the Supreme Court must preside over the Senate trial of an impeached president, can the Chief Justice delay such a trial by resigning?
No, the powers and duties [of the chief justice] shall devolve upon the associate justice next in precedence who is able to act.1 It appears that, in that scenario, Justice Clarence Thomas would become the presiding officer in the impeachment trial.2
1 28 U.S. Code § 3.Vacancy in office of Chief Justice; disability.
Whenever the Chief Justice is unable to perform the duties of his office or the office is vacant, his powers and duties shall devolve upon the associate justice next in precedence who is able to act, until such disability is removed or another Chief Justice is appointed and duly qualified.
2 Associate Justice of the Supreme Court of the United States.
Associate justices have seniority by order of appointment, although the chief justice is always considered to be the most senior. If two justices are appointed on the same day, the older is designated the senior justice of the two. Currently, the senior associate justice is Clarence Thomas.