During the Indian Nationalist Movement, there were several instances where individuals attempted to assassinate British officials in order to protest against colonial rule. In this particular question, the person who made an attempt on the life of Kingsford, a District Judge, was Khudiram Bose and Prafulla Chaki.

Option 1: Chidambaram Pillai - Chidambaram Pillai was a prominent figure in the Indian Nationalist Movement in South India, particularly in Tamil Nadu. However, there is no evidence or historical records to suggest that he was involved in the attempt on the life of Kingsford.

Option 2: Damodar and Balkrishna Chapekar - Damodar and Balkrishna Chapekar were Hindu revolutionaries who were active in the early 20th century. They were known for their involvement in the assassination of British officials, but there is no evidence to suggest their connection to the attempt on Kingsford`s life.

Option 4: Vanchj Aiyar - There is no historical evidence or records of Vanchj Aiyar being involved in any attempts to assassinate British officials during the Indian Nationalist Movement.

Therefore, the correct answer is option 3: Khudiram Bose and Prafulla Chaki.