Researchers have created innovative technological solutions to support people with common chronic illnesses. In this study, we investigate design opportunities for people with rare diseases who are not well studied or have smaller populations to work with, because although an individual's disease may be rare, the number of people living with a rare disease is substantial. We conducted an interview study with 19 individuals with rare diseases from around the world to understand common problems and experiences that could be supported through design. We found that communicating with friends, family, and providers about her disease were challenges for participants. Additionally, participants thought of their disease as being a large part of who they were. We discuss these findings in the context of prior work on common chronic illnesses, addressing the potential relevance of existing technological interventions for people with rare diseases.