The exclusive co-ed private school in Hartford to which Rory gains a late acceptance, kicking off the events of the entire Gilmore Girls series. It is loosely based on Choate Rosemary Hall, a private boarding school in the town of Wallingford, Connecticut.
The name Chilton may have been inspired (in universe) by Mary Chilton (1607-1679), a Pilgrim who came to America from England on the Mayflower, giving the name a historical connection; Mary Chilton was an ancestor of George Bush and George Bush Jr. According to legend, Mary was the first passenger to step ashore at Plymouth in 1620, excitedly jumping out of the boat and wading out to Plymouth Rock. It seems like a name suitable for daring young girls willing to leap into a new world.
For the 2017-18 academic year, Choate’s tuition fees for a day (non-boarding) student were $44 400. However, they have a generous financial aid package which would mean that someone in Lorelai’s situation would have their tuition fees heavily subsidised. You can also pay by the month with no interest, and unlike Chilton, there is only a small enrolment fee.
It is unclear why Chilton never offered any similar financial aid to Rory – perhaps because she was a late acceptance. For the purpose of the plot it was necessary for Lorelai to be desperate for money, or Gilmore Girls could never have happened. So Chilton had to be a price-gouging school with massive enrolment fees, no financial aid, no payment plans, and no up-front information about their fees for parents (Lorelai is apparently disconcerted to learn Chilton costs anything at all).
Exterior scenes at Chilton were filmed at Greystone Mansion in Beverly Hills, California; this 1920s Tudor-style mansion is in a public park owned by the City of Beverly Hills, and is a popular place for film and TV locations.