I would suggest talking to your hotel concierge and once you get an approx rate, then start calling some tour agencies....this way at least you know the ballpark figure....they have different rates for tourist and normal people...

everything in India is negotiable.....so you can negotiate on the price given....also stick with an AC car..Chennai will be hot and humid...traffic is BAD..so is the pollution....if you are stuck in traffic, you do not want to suck in pollution equivalent to 3 packs of cigarrettes a day...