Several caravans have parked in Sainsbury’s supermarket on Rother Way and are taking up a number of spaces including disabled bays and those for parents with children, outside the store.
A resident, who wished to remain anonymous, said they had been told by management that the caravans had arrived before the shop opened.
They added: “The world has come to something when people can behave as they please and ignore ALL the rules that the rest of us follow.
"When I am faced with this sight in a supermarket car park, it takes the biscuit as to what world some people think we live in.
“Management at Sainsbury’s Rother Way, say there is nothing they can do and the Police know about it.”
A Sainsbury’s spokesperson said: “We’re monitoring the situation and are in touch with the local authorities.”
Derbyshire Constabulary spokesman added: “We received a call on around 1.20pm today (6 May) reporting that a group of travellers had moved onto the car park at Sainsbury’s on Rother Way at Chesterfield.
"Officers have visited the car park to liaise with the group and store staff.
“We are continuing to monitor the situation.”
Shoppers reported around 12 caravans are now parked in the store’s car park.