Strolling through Palace Costume is a bit like stepping into a Tim Burton movie. Everywhere you turn, there’s a surreal riot of outrageous outfits, from over-the-top Beetlejuice-style attire to Ed Wood-ish 1950s dresses to paste jewelry in a rainbow of Pee-Wee tints.

In fact, a lot of the costumes found in Burton’s movies were sourced from these very racks, along with outfits appearing in hundreds of other films. Forrest Gump, Once Upon a Time in Hollywood, Everything Everywhere All at Once, Austin Powers, The Big Lewbowski, Don’t Worry Darling — they all featured clothing that was pulled from Palace Costume, known among Hollywood stylists as “the Louvre of vintage.”

Owner Melody Barnett in the 1970s with her cat Star Baby.

“It started 60 years ago,” says owner Melody Barnett, as she shuffles through room after room filled with fashion history. “I found a box of Victorian clothes at a...