The arm of government that appoints the Chief Justice is

The question asks: "The arm of government that appoints the Chief Justice is"

In a system of government with separation of powers, the Executive arm is typically responsible for appointing high-ranking judicial officials, such as the Chief Justice. This appointment often requires confirmation by the Legislative arm.

In Nigeria, the President, who heads the Executive arm of government, appoints the Chief Justice of Nigeria, subject to confirmation by the Senate (part of the Legislative arm). Therefore, the primary appointing authority is the Executive.

The final answer is $\text{Executive}$