The shooting took place around 11.30 p.m. when two men attacked Meenakshi, wife of a retired engineer, and tried to snatch her chain while she was opening the gate of her house.
When she resisted and raised an alarm, the bike-riding looters opened fire and shot her in stomach and leg.
The attackers then fled and are yet to be arrested.
Police are readying sketches of the culprits on the basis of information given by a neighbour, an official told IANS.
The injured woman was admitted to a hospital and is likely to be operated later in the day. She is out of danger, said docors.
Chain snatching has become a major menace in the state capital in the last few years.