This is a temple of Thillai Kali Amman Temple.
There is not a proper place to sit and meditate. You can go into meditative states here effortlessly.
How to get there:
The temple is located at the heart of Chidambaram.
Map: https://goo.gl/maps/NiKT3ie1EoAeDRCp7
About Thillai Kali Temple
The temple is on the outskirts of the city of Chidambaram. Legend says that the goddess Kali (a form of Parvati) moved here after losing to the god Shiva in the celestial dance contest.
It was an argument that who is superior, either Shiva or his wife Parvati. In order to resolve thus, they performed a dance program at Chidambaram in front of Vishnu, Brahma and other deities. While they were playing dance, Shiva was about to be defeated.[1]
Shiva performed the Urdhva Tandava posture, i.e. raising one leg above his head and challenged Parvati to replicate it. Due to her modesty and shyness, Parvati refused and agreed her defeat.
Parvati in anger assumed her ferocious form Kali and left Chidambaram (Thillai) and settled outside the town borders. Thus, she is worshipped as Thillai Kali here. Her anger was pacified by Brahma by chanting the Veda and praising her.
Kali was pleased and assumed a benign form with four heads similar to Brahma and known as Thillai Amman (Mother of Thillai) or Brahma Chamundeeswari.
There are two main shrines in the temple. The west-facing shrine depicts the goddess in his benign four-faced form Brahma Chamundeeswari.
In the east-facing shrine, the goddess appears in her ferocious form called Thillai Kali.
The other important shrines are for goddess Saraswati as Veena Vidyambigai and for Dakshinamurthy (a form of Shiva) where he has a female form called Kadambavana Dhakshina Rupini.[2]
Source:
https://en.wikipedia.org/wiki/Thillai_Kali_Temple,_Chidambaram