Option 1: Asaf Jah II - This option suggests that Asaf Jah II established himself as an independent ruler with the title of Nizam-ul-Mulk Asaf Ja at Hyderabad. However, this is incorrect as Asaf Jah II was the successor of Nizam-ul-Mulk Asaf Ja, not the founder of the dynasty.

Option 2: Bahadur Shah - This option does not provide any relevant information to the question. Bahadur Shah was a Mughal emperor and does not have any connection to the establishment of an independent rule at Hyderabad.

Option 3: Alivardi Khan - This option suggests that Alivardi Khan established himself as an independent ruler with the title of Nizam-ul-Mulk Asaf Ja at Hyderabad. However, this is incorrect as Alivardi Khan was the Nawab of Bengal and Bihar, not the ruler of Hyderabad.

Option 4: Chin Khilich Khan - This is the correct option. Chin Khilich Khan, also known as Nizam-ul-Mulk, established himself as an independent ruler with the title of Nizam-ul-Mulk Asaf Ja at Hyderabad. He founded the Asaf Jahi dynasty, which ruled the Hyderabad State from 1724 to 194