Kantner was born in San Francisco, California, the daughter of two Jefferson Airplane and Jefferson Starship bandmembers, singer Grace Slick (born Grace Wing) and guitarist Paul Kantner. She is a native of San Francisco, living first in the city itself, and later in Mill Valley, just north of the city, and is an alumna of Tamalpais High School in Mill Valley, California and Redwood High School, Larkspur, California. She has an older half-brother, Gareth Alexander Kantner, who works in the film industry, and a younger half-brother, Alexander Kantner, who occasionally appears on-stage with Jefferson Starship playing bass guitar.