Meat, seafood, vegetables in Chennai?

Hi,

This far we have been eating mostly out, but I'd like to do more of my own cooking. I'd appreciate recommendations for good shops for meat, seafood and vegetables.

Amma Nana has decent chicken, but selection is limited and availability is not always there. We have bought seafood once or twice from the market next to Marina Beach, but I'd like to have a somewhat less exotic alternative. There are small local fruit and vegetable shops everywhere; they are nice, but the selection is very limited.

Thanks,
Mikko