The correct answer to the question is option 2, the Brhadisvara temple at Thanjaur. Chola architecture refers to the architectural style developed by the Chola dynasty in South India during the 9th to 13th centuries. The Cholas were known for their grand and intricate construction of temples.

Option 1, the Subrahamanya temple at Thanjaur, is not the most elaborate temple of Chola architecture. While it may be a significant temple, it does not hold the same level of grandeur as the Brhadisvara temple.

Option 3, the Temple of Kailashanatha at Kanchipuram, is another notable temple, but it does not surpass the magnificence of the Brhadisvara temple in terms of Chola architecture.

Option 4, the temple at Gangaikonda Cholapuram, is also a significant temple built by the Cholas. However, it is not considered the finest and most elaborate temple of Chola architecture.

Therefore, the Brhadisvara temple at Thanjaur is considered the finest and most elaborate temple of Chola architecture, showcasing the intricate craftsmanship and architectural brilliance of the Chola dynasty.