Police say the incident took place at 9:55 a.m. on June 12th.
The 57-year-old victim was riding on the route 38 SEPTA bus when it stopped at Broad and Chestnut streets.
Police say the suspect, who was seated behind the victim, was exiting the bus when he snatched the woman's gold chain from her neck.
The suspect fled the bus on foot west on Chestnut Street.
The victim suffered a laceration on her neck.
The suspect is described as a black male, with a thin build, 5'11-6'1, thin goatee, wearing a black Pittsburgh Pirates baseball cap, dark blue t-shirt with a Nike logo on the front and dark colored shorts.
Anyone with information is asked to contact Philadelphia Police at 215-686-TIPS (8477), text a tip to PPD TIP (773847) or through PhillyPolice.com.