The incident happened around 8 p.m. on September 25.
Surveillance pictures show the moment the suspect pulled a gun on a clerk inside the Stop & Shop Deli on Crooked Hill Road in Brentwood.
Police say the clerk then pulled out a machete and chased the robber out of the store northbound through the parking lot.
No one was hurt.
Authorities say the man didn't get away with any cash.
The suspect was described as a young, black man, with a thin build, approximately 5 foot 10 inches tall. He was wearing a gray mask, a black running-style top with white stripes on the sleeves, dark pants and black and white sneakers. He was carrying a black Air Jordan backpack and a silver .22 caliber pistol.
Suffolk County Crime Stoppers offers a cash reward of up to $5,000 for information that leads to an arrest. Anyone with information about this crime is asked to call anonymously to Crime Stoppers at 1-800-220-TIPS. All calls will be kept confidential.