The correct answer is A. Governor.
The Governor is the head of the state and is appointed by the President of India. The Governor appoints the Chief Minister of the state on the basis of the majority party or coalition of parties in the Legislative Assembly.
The Chief Justice of the Supreme Court is the head of the judiciary and is appointed by the President of India. The Chief Justice of the High Court is the head of the High Court and is appointed by the President of India on the recommendation of the Chief Justice of the Supreme Court.
The Chief Justice of the High Court does not have any role in the appointment of the Chief Minister.