Police said the incident happened at about 5.30pm when three young men wearing balaclavas were seen in West Street.
A police spokesperson said: “They approached a 15-year-old boy who was sat with a friend outside the Lynd Cross public house and Wilkinson store.
“The boy was then taken around the corner towards The Gym, and his bag was taken.”
One of the three suspects was described as a slim white man, 6’2” and was seen carrying a knife, police said.
The police spokesperson added: “Members of the public saw what happened and intervened, challenging this suspect and then bravely helping to detain him in a nearby Waitrose store after a short pursuit.”
Police said this suspect was then arrested and that now officers want to identify the other two young men in connection with the incident.
A police spokesperson said: “One of the young men is described as black and 5’2”. The second young man is described as mixed race and 5’4”.
“Officers have appealed for witnesses; anyone who recognises the two young men; or anyone who may have seen them in the town centre on July 15, to come forward.”
People can report information to Sussex Police online or by calling 101, quoting serial 1144 of 15/07.
Alternatively members of the public can contact CrimeStoppers anonymously on 0800 555 111.