Hills was born in October, 1953, to a family of missionaries in India and grew up in Michigan. She studied at Interlochen, where she played in a band with Chris Brubeck and Peter Erskine. In 1976, she moved to Chicago and was a co-founder of the record label Hogeye Music. After releasing a few records on Hogeye, the label was bought out by Flying Fish Records in the mid-1980s. In 1984, Anne briefly was a member of a trio (along with Tom Paxton and Bob Gibson) known as the Best of Friends.