The Union Constitution Committee of the Constituent Assembly was tasked with shaping the structure and functions of the government of India as stated in the Constitution.

Option 1, B. R. Ambedkar, was not the chairman of this committee but served as the chairman of the drafting committee of the Indian Constitution.

Option 2, J. B. Kripalani was an important member of the Constituent Assembly, however, his role was not that of the chairman of the Union Constitution Committee.

Option 3, Jawaharlal Nehru, is the correct choice, as he was the chairman of the Union Constitution Committee. Nehru, who would later serve as India`s first Prime Minister, played a crucial role in sculpting the Union Constitution, hence was made the chairman.

Option 4, Alladi Krishanaswami Ayyar, also a critical figure in the forming of the Indian Constitution, was not the chairman of the Union Constitution Committee but served in the drafting committee under B.R. Ambedkar.

In conclusion, the chairman of the Union Constitution Committee of the Constituent Assembly was Jawaharlal Nehru.