A chaise is a type of closed carriage seating up to three people.
The “Four” refers to the number of horses pulling the carriage.
However, most chaises only had two horses pulling it as that was more economical. Four horses are expensive!
When Mrs. Bennet mentions to Mr. Bennet that Mr. Bingley has a chaise and four, this is to impress upon his wealth. He has enough money to throw around that he has four horses pulling his carriage!
