The correct answer is option 1, Srirangam. Srirangam is a temple that belongs to the Vaishnavite tradition.

Let`s analyze the other options to understand why they are not the correct answer:

Option 2, Chidambaram, is a temple dedicated to Lord Shiva and follows the Shaivite tradition. The temple is famous for its Nataraja statue, representing Lord Shiva as the cosmic dancer.

Option 3, Gangaikonda Cholapuram, was built by the Chola king Rajendra I after his successful campaign in northern India. This temple is also dedicated to Lord Shiva and follows the Shaivite tradition.

Option 4, Thanjavur, refers to the Brihadeeswara temple, also known as the Big Temple. This temple is dedicated to Lord Shiva and is part of the Shaivite tradition.

Therefore, the only correct option that belongs to the Vaishnavite tradition is option 1, Srirangam. Srirangam is a prominent temple in Tamil Nadu and is dedicated to Lord Ranganatha, a form of Lord Vishnu. It is one of the most important pilgrimage sites for Vaishnavites.