In Chennai the beat engineering university are

1. VIT Vellore

2. VIT chennai

3. SRM

4. IIT Madras

And many more....

You can prefer below  links in order to see the top 10 engineering universities in Chennai-

https://collegedunia.com/engineering/chennai-colleges.

http://admissionsinchennai.in/admissions/engineering-admissions-top-engineering-colleges-tamilnadu-chennai-2016/

Iit madras

Madras institute of technology.