Gunn was born in Cleveland, Ohio, but moved at an early age and was raised in Santa Fe, New Mexico, the daughter of Sharon Anna Kathryn "Shana" Gunn (née Peters), an interior designer, and Clemens Earl Gunn Jr. , who worked in real estate. She graduated from Santa Fe Preparatory School in 1986. She attended Northwestern University, where she majored in theater and graduated in 1990. During fall of 1988, Gunn spent a semester abroad to study at the British American Drama Academy. After moving to Laurel Canyon, Los Angeles, she shared a house with Pamela Adlon.