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As per your query... there is no college who are offering UG course with integrated UPSC IAS coaching in Chennai, you can study in coaching centre along with college, you can take course in college which help you while preparing UPSC exam.

here is the list of best coaching institute for UPSC in Chennai:

• Plutus IAS Coaching Institute
• Ganesh’s ias Coaching institute, Anna Nagar, Chennai
• Shankar IAS Academy
• All India Civil Services coaching
• Smart Leaders IAS Academy

For more information about UPSC IAS exam checkout given link below:
https://competition.careers360.com/exams/upsc-cse

Hope you found it helpful
All the best!!!