There are many Coaching Institutes in Chennai for IIT JEE preparation. I am providing contact details of best Coaching Institutes for your reference:

Aakash Institute  
Address: No. 20, North Park Street, Venkatapuram,
Above Karnataka Bank, Ambattur,
Chennai, Tamil Nadu 600053
Phone: 044 3945 4545

ICT Academy  
Address: 44A, GST Road, Near Guindy Railway Station,
Chennai, Tamil Nadu 600032
Phone: 098410 98611

Aakash Institute
Address: 3rd Floor, K.R.Building No.-12, L.B. Road,
Adyar Circle, Adyar, Chennai, 600020
Phone: 044 4353 0689

Conceptree Learning Nanganallur
Address: No. 21, 27th StreetThillaiganga Nagar ,
Nanganallur, Chennai, Tamil Nadu 600061
Phone: 099620 26039

Anugraham Classes  
Address: Manikkam St, AGS Colony, Ramakrishnapuram,
West Mambalam, Chennai, Tamil Nadu 600033
Phone: 044 2474 9441

Science and Mathematics Academy for Real Talents  
Address: New No. 2, Old No. 11, Hastagiri Street,
Samiyar Madam, West Mambalam, Chennai, Tamil Nadu 600033
Phone: 095000 23248

Emphasis IIT JEE Academy  
Address: Near Bus Depot, 23, Chennai - Tiruttani Hwy,
Vasantham Nagar, Avadi, Tamil Nadu 600054
Phone: 088073 50802

FIITJEE Towers  
Address: No 51, Fiitjee Towers, DR Ramasamy Salai,
KK Nagar, Chennai, Tamil Nadu 600078
Hours: Open today • 5AM–8PM
Phone: 095000 43608

TRS IIT CLASSES  
Address: 37/72, 7th Avenue, Ashok nagar,
(opp. GRT School Play Ground)
Chennai, Tamil Nadu 600083
Hours: Open today • 10AM–5PM
Phone: 094443 61199

Rit Academy  
Address: 91, Karuneegar Street, Opposite To Kamala Textiles,
Adambakam, Paramesh Nagar, Adambakkam,
Chennai, Tamil Nadu 600088
Phone: 098409 39640

SPECTRUM  
Address: No 2 Rajan street Near to ICICI BANK
Bazullah road T Nagar, Chennai, Tamil Nadu 600017
Hours: Open today • 10AM–9PM
Phone: 098407 60244