In India, the appointment of Judges of the High Court of a State is done by the President. This power is derived from Article 217 of the Indian Constitution. The President acts upon the advice of the Chief Justice of India, the Governor of the concerned State, and the Chief Justice of the concerned High Court in making these appointments.

Option 2, The Vice-President, is not involved in the appointment of Judges of the High Court. The Vice-President`s role is primarily in the functioning of the Rajya Sabha, the upper house of the Indian Parliament.

Option 3, The Chief Justice of India, does play a significant role in the process as the President acts upon their advice. However, the actual appointment is made by the President.

Option 4, The Governor, also plays a role in the appointment process as their recommendation is considered by the President. However, the Governor does not have the direct power to appoint Judges of the High Court.

Therefore, the correct answer is option 1, The President.