No worries I will provide you Central Government of India approved list of research institutes located in Chennai, so that you can remember easily.

Here I have some names of institutes

Central Institute of Brackish Water Aquaculture
Central Institute of Plastics Engineering & Technology
Central Leather Research Institute
Indian Institute of Technology (IIT)
Indian Maritime University
Indian Statistical Institute
Institute of Mathematical Sciences (IMSc)
National Institute of Electronics & Information Technology (NIELIT)
National Institute of Fashion Technology
National Institute of Malaria Research
National Institute of Ocean Technology
National Institute Of Technical Teachers Training and Research

Apart from them I have some more names

Indian Institute of Chemical Technology
Indian Institute of Management
Indian Institute of Remote Sensing (IIRS)
Central Sheep and Wool Research Institute
National Institute of Public Finance and Policy
Indian Institute of Petroleum and Energy
National Academy of Construction
Institute of Economic Growth
National Institute of Industrial Engineering (NITIE)
Indian Institute of Engineering Science and Technology (IIEST)
Indira Gandhi Institute of Development Research
Central Institute of Plastics Engineering & Technology
National Institute of Malaria Research
National Brain Research Centre (NBRC)
Central Institute of Educational Technology
National Institute of Mental Health and Neurosciences (NIMHANS)
National Institute of Water Sports
National Institute of Oceanography (NIO)
Indian Institute of Science (IISc)
State Institute of Public Administration and Rural Development
National Institute of Design
National Institute of Homoeopathy (NIH)
National Institute of Technology
Central Drug Research Institute
Indian Statistical Institute
Centre for Development Studies
Central Institute for Cotton Research
Central Electronics Engineering Research Institute
National Institute of Science Education and Research (NISER)
Indian Veterinary Research Institute
Tata Institute of Fundamental Research (TIFR)
Institute of Food Security
All India Institute of Medical Sciences (AIIMS)
Raman Research Institute (RRI)
Institute of Rural Management
Central Institute of Psychiatry
Indian Institute of Mass Communication (IIMC)
College of Defence Management
Indian Maritime University
Indian Institute of Natural Resins and Gums (Indian Lac Research Institute)
Aryabhatta Research Institute of Observational Sciences (ARIES)
International Institute for Population Sciences
Rajiv Gandhi Institute of Petroleum Technology
National Sugar Institute
Indian Institute of Technology (IIT)
National Institute of Construction Management and Research
Indian Institute of Petroleum
Saha Institute of Nuclear Physics
Indian Institute of Ecology and Environment
National Institute of Open Schooling
Indian Association for the Cultivation of Science (IACS)
National Power Training Institute
Harcourt Butler Technological Institute
National Academy of Agricultural Research Management
Indian Institute of Information Technology (IIIT)
Indian Agricultural Research Institute (IARI)
National Institute of Hydrology
Indira Gandhi Centre for Atomic Research (IGCAR)
Central Glass and Ceramic Research Institute (CGCRI)
National Academy of Customs Excise and Narcotics (NACEN)
Lakshmibai National University of Physical Education (LNIPE)
National Institute of Fashion Technology
Indian Institute of Information Technology and Management
Central Institute of Road Transport (CIRT)
Indian Institute of Forest Management (IIFM)
Central Institute of Indian Languages
Institute of Physics
Indian Institute of Tourism and Travel Management
Central Institute of Agricultural Engineering
National Institute of Electronics & Information Technology (NIELIT)
Central Institute of Fisheries, Nautical and Engineering Training (CIFNET)
National Institute of Animal Welfare
National Institute of Securities Markets (NISM)
National Institute of Rural Development
Indian National Centre for Ocean Information Services
Indian Institute of Spices Research
Indian Institute of Tropical Meteorology
Indian Institute of Astrophysics
Central Institute of Technology, Kokrajhar (CIT)
Central Research Institute for Dryland Agriculture
Central Leather Research Institute
Indian Institute of Soil Science
Central Institute of Medicinal and Aromatic Plants
Indian Institute of Science Education and Research (IISER)
Indian Institute of Foreign Trade (IIFT)
Rajiv Gandhi National Institute of Intellectual Property Management Nagpur
Maulana Abul Kalam Azad Institute of Asian Studies
Sher-i-Kashmir Institute of Medical Sciences
National Institute of Ocean Technology
National Museum Institute of the History of Art, Conservation and Museology (NMIHACM)
Centre for Excellence in Basic Sciences
Institute of Genomics and Integrative Biology (IGIB)
Centre for Cultural Resources and Training (CCRT)
Central Soil Salinity Research Institute
Central Mine Planning and Design Institute Limited
National Tuberculosis Institute
Sant Longowal Institute of Engineering and Technology(SLIET)
National Institute of Foundry and Forge Technology(NIFFT)
National Botanical Research Institute (NBRI)
National Institute of Disaster Management
National Institute Of Technical Teachers Training and Research
Central Institute of Fresh Water Aquaculture
All India Institute of Speech and Hearing (AIISH)
National Institute of Agricultural Extension Management
Satyajit Ray Film and Television Institute
Indian Diamond Institute
Sanjay Gandhi Postgraduate Institute of Medical Sciences
School of Planning and Architecture
National Institute of Homoeopathy
Harish Chandra Research Institute (HRI)
Institute of Defence Studies and Analyses
PEC University of Technology (PEC)
Indian Institute of Architects
National Institute of Urban Affairs
Indian Institute of Pulses Research
Indian School of Mines
Birbal Sahni Institute of Palaeobotany
S.N. Bose National Centre for Basic Sciences (SNBNCBS)
National Institute of Science Communication and Information Resources (NISCAIR)
National Dairy Research Institute
V. V. Giri National Labour Institute
Indian Institute of Social Welfare and Business Management
Central Institute of Brackish Water Aquaculture
Netaji Subhas National Institute of Sports (NSNIS)
Institute of Mathematical Sciences (IMSc)
National Defence College of India
Physical Research Laboratory (PRL)
National Environmental Engineering Research Institute
National Institute of Pharmaceutical Education and Research
Central Institute of Fisheries Education
National Institute of Nutrition
Institute for Plasma Research (IPR)
Variable Energy Cyclotron Center
National Academy of Agricultural Sciences
Indian Institute of Plantation Management
Indian Institute of Chemical Biology (IICB)
Institute for Studies in Industrial Development
National Institute of Science Communication and Information Resources
Centre for the Study of Developing Societies (CSDS)
Film and Television Institute of India
Central Food Technological Research Institute
Foreign Service Institute
National Civil Defence College
Indira Gandhi National Forest Academy (IGNFA)
Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR)
National Institute of Agricultural Marketing
Indian Institute of Space Science and Technology (IIST)
Morarji Desai National Institute of Yoga
Tata Institute of Social Sciences
Bose Institute
Institute of Secretariat Training and Management
Institute for Studies in Industrial Development
North Eastern Regional Institute of Science and Technology (NERIST)