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An Associate Justice can be nominated to be Chief Justice, but they need to be confirmed again just like a fresh appointment. Rehnquist is a recent example.

• atonse 7y ago
  I thought of this when I posted that ("I guess technically an existing judge could resign and be re-nominated"). Could've saved some downvotes :-)
  • pc86 7y ago
    They don't have to resign. Yes they need to be confirmed again but it's as much a "promotion" as any other.