The piece, which shows a girl building sandcastles with the word Tesco on them, appeared earlier this week just down from Marine Court.
It is on the back of one of the steps which lead down to the shingle beach and has already attracted admiring glances from passers-by.
And the Observer can reveal it is almost definitely an original Banksy piece.
Banksy's close friend Ben Eine lives nearby and was celebrating his 40th birthday last weekend - with Banksy in town to join in.
And Banksy experts at Art Republic in Brighton confirmed the piece was almost certainly his work.
Andrew Milledge told the Observer: "We have stocked Banksy prints for many years and this work certainly has many of the hallmarks of his previous street art."