Big Hat was a Chicago band founded in the late 80s by a fellow named Preston Klik. His compatriots: Yvonne Bruner, Char Malloy (also known as Char-Malloy Baum), and James Stallman. I've always found their sound very hard to categorize - there are ethereal, middle eastern, and world beat elements, among other things, and the band was favored by many Chicago goths.
Sadly, Big Hat broke up in 1994. As Preston put it, "The fat lady has sung," but he and Yvonne went on to form My Scarlet Life. Char Malloy has done some side work with Material Issue and another of Preston's side projects: Bed Of Roses, on the album The Kissing Tree. Jim Stallman did some percussion work with the band Catherine. However, it doesn't look like Char or Jim are very active in music right now.