The correct chronological order of the formation of the following as full States of the Indian Union is Option 2: Nagaland-Haryana-Sikkim-Arunachal Pradesh. Here`s the reasoning behind this answer:

1. Nagaland: Nagaland became a full state of the Indian Union on December 1, 1963. It was initially established as a separate state within the Indian Union under the State of Nagaland Act, 1962. This Act recognized the unique cultural and historical aspects of Nagaland and granted it statehood.

2. Haryana: Haryana was formed as a separate state on November 1, 1966. It was carved out of the existing state of Punjab to address regional linguistic and cultural differences. The Punjab Reorganization Act, 1966, was enacted to create Haryana as a distinct state.

3. Sikkim: Sikkim joined the Indian Union as a full state on May 16, 1975. Prior to its merger, Sikkim was a protectorate of India. A referendum held in Sikkim in 1975 resulted in a majority vote in favor of joining India. Subsequently, the 35th Amendment Act of the Indian Constitution was enacted to incorporate Sikkim as a state of the Indian Union.

4. Arunachal Pradesh: Arunachal Pradesh became a full state of the Indian Union on February 20, 1987. It was earlier known as the North-East Frontier Agency (NEFA) and was administered as a union territory. The statehood for Arunachal Pradesh was granted through the State of Arunachal Pradesh Act, 1986, after considering the region`s historical and geographical context.

It is important to note that the chronological order is based on the dates of full statehood being granted to these regions. The option that correctly represents this order is Option 2: Nagaland-Haryana-Sikkim-Arunachal Pradesh.