Airtel , Aircel & Vodafone are the 3 private operators in Chennai which have 3G. All 3 have decent coverage within the city & if you are looking to use it at home, I would say you can go for a service provider who has good connectivity even when normally using the phone. A friend uses Vodafone in Velachery and its quite good. Though Aircel is likely to be the cheapest amongst the three.