"he came down on Monday in a chaise and four"
A May Morning in the Park
Public DomainA May Morning in the Park - Credit: Thomas Eakins (1844-1916)

A chaise, from the French for chair, is a small light carriage. Some have two wheels, pulled by one or two horses; others have four wheels with as many horses.

This particular quote implies a chaise and four horses. It is mentioned by Mrs Bennet as it shows how wealthy Mr Bingley is.