The theft happened at the Acme Market at 1901 Concord Pike in the Fairfax Shopping Center around 4:00 p.m. Monday.
Police say the suspect was seen on surveillance video grabbing the purse from the victim's cart and leaving the store.
The suspect is described as a white woman, 25 to 30 years old, standing 5'7" to 5'9" tall and weighing 130 to 140 pounds. She was wearing a black coat with fur around the hood, jeans and white sneakers.
Anyone with information is asked to call Delaware State Police at 302-761-6677.