The incident occurred yesterday when Priyanka Goyal, a resident of Avantika in Rohini, had gone to Sector 6 market.
While she was walking on the road near Vishram Chowk, two bike-borne men came from behind and one of them snatched her gold chain, the police said.
She caught hold of one of them and sought help from a passersby but no one came to help her since the accused was carrying a firearm, they said.
After firing at her, the accused pushed her with his leg and fled from the spot, the police said.
Ms Goyal followed him and managed to catch hold of the collar of the pillion rider. He hit her with the pistol and threatened to fire at her, the police said.
He shot her in the leg and the duo fled from there with the chain. The police were informed and she was taken to a hospital where her condition is critical, they added.
The accused were not wearing helmets, the police said, adding, they are scanning the CCTV footage from the area to identify them.