From "The Girls' Life: Guide to Growing Up"? ;) It's the made-up name of a restaurant. The "Chez (name)" pattern is often used for expensive (French) restaurants. In this context, the name "Chez Paris" suggests that the restaurant is exceptionally haughty and snooty ("any typical high-class French restaurant"), and would turn away guests who arrive after the time they had booked.

Within the context you might find a reason this name in use. To give a table to someone else likely means that the table should have gone to someone on a 'first come first serve' basis. Whoever was first is being slighted.

"Chez Paris" seems to be a name in this sentence... (like the name of team or a group of people maybe?)