It happened Thursday afternoon while the woman was shopping at Shoprite on the unit block of Chestnut Hill Plaza.
Authorities say the suspect followed the victim around the store and grabbed her purse from the shopping cart.
The purse contained an undisclosed amount of cash and the woman's car keys.
Surveillance video captured the suspect fleeing the parking lot in the victim's vehicle.
The victim's vehicle is described as a 2006 Mercury Grand Marquis, silver in color, four door, white wall tires and silver rims. Vehicle displays Delaware Registration #133567. The vehicle has not yet been recovered.
The suspect is described as an African-American male, 20-30 years of age, 5'06"-5'08" tall, 190-220 pounds, with a large build. He was last seen wearing dark zippered hooded sweatshirt with "ECKO UNLTD" and gray sweat pants.
Anyone with information is urged to contact Delaware State Police Troop 6 at 302-633-5000 or by using the Delaware State Police Mobile Crime Tip Application available to download at: http://www.delaware.gov/apps/.
Information may also be provided by calling Delaware Crime Stoppers at 1-800-TIP-3333, via the internet at www.tipsubmit.com, or by sending an anonymous tip by text to 274637 (CRIMES) using the keyword "DSP."