Barnes Peacock was the first Chief Justice of the High Court. He assumed the charge when the court was founded on 1 July 1862. Romesh Chandra Mitter was the first Indian officiating Chief Justice, and Phani Bhushan Chakravartti was the first Indian permanent Chief Justice of the court. 

Further Reading:

• List of High Courts in India
• Types of Writs in India
• Supreme Court of India

To read more about the Powers And Functions Of the High Court, check the linked article.