The Cornish National Liberation Army has apparently labelled the pair, who have set up restaurants in the county, as "newcomers" and "outsiders", in an e-mail.
The message states that residents of Padstow, where Stein owns a string of businesses, have approached the radical organisation “for assistance”.
It labels television chef Stein “this English newcomer” and says it is “common knowledge” he and his firms are “held in contempt” by locals.
The e-mail adds: “His vehicle and those of his clients and customers are also bona fide targets for our activists”.
Meanwhile Oliver, who set up one of his Fifteen restaurants at Watergate Bay, is described as “another incomer who has caused the inflation of house and other living costs at Cornish expense”.
Devon and Cornwall Police told the Western Morning News newspaper they were treating the messages “very seriously” and would “vigorously investigate any premeditated or publicised planned criminal activity”.