Peters was born into a Sicilian-American family in Ozone Park in the New York City borough of Queens, the youngest of three children. Her mother, Marguerite ("née" Maltese), started her in show business by putting her on the television show "Juvenile Jury" at the age of three and a half, and her father, Peter Lazzara, drove a bread delivery truck. Her siblings are casting director Donna DeSeta and Joseph Lazzara. She appeared on the television shows "Name That Tune" and several times on "The Horn and Hardart Children's Hour" at age five.