In this paper, we motivate and introduce Futuristic Autobiographies, a method inspired by design fiction for eliciting values and perspectives on the future of technologies from participants such as users, designers, and researchers. Futuristic autobiographies are the creative work of the researchers and participants. Grounded in empirical and background work, researchers pose several stories involving the participant as a character about a future state with robots. Participants are then asked to weave fictional autobiographies to explain what led to this future state. Via a case study in which futuristic autobiographies were used with 23 roboticists, we detail the process involved in developing and implementing this method. When futuristic autobiographies are employed and carefully crafted from background research, they allow informants to speak for themselves on how their practices and values are intertwined now and in the future. We highlight both the benefits and challenges of futuristic autobiographies as a way to elicit rich stories about values. We argue that futuristic autobiographies are a promising addition to the current qualitative methods toolkit used in HRI.