The incident occurred at 9:02 a.m. Saturday at the Wawa on the 4600 block of Ogletown Stanton Road in Newark.
Police say two men entered the store, loitered around the cash registers, and when no one was near, stole three packages of cigarettes.
Both suspects then began to run out of the store when a 57-year-old Newark man entered.
One of the men pushed the customer aside and the two suspects fled.
Authorities say the 57-year-old realized the suspects had just stolen from the store, so he returned to his truck and tried to follow the suspects, catching up to them on Brownleaf Road in the Hillside Heights Development.
As the man chastised the suspects for stealing, police say one suspect removed a baseball bat from the bed of the man's truck and smashed the truck's side view mirror.
The same suspect then threatened the 57-year-old with the bat, and both suspected thieves fled on foot.
Delaware State Police is asking anyone who may have any information in reference to this incident to contact at Troop 6 at 302-633-5000 extension 801.