N.H. Rev. Stat. Ann. § 490:1

The supreme court shall consist of 5 justices appointed and commissioned as prescribed by the constitution. On the effective date of this section, the administrative position of chief justice shall be held by the justice with the most seniority on the court for a period of up to 5 years. Each succeeding chief justice shall serve for a period of up to 5 years and shall be the justice with the most seniority of service on the court who has not yet served as chief justice. A justice may decline to serve as chief justice; however, no justice shall be permitted to serve successive terms as chief justice. In the event that all 5 justices have served a term as chief justice, succeeding chief justices shall serve rotating 5-year terms based on seniority.