In chronic conditions, patients and providers need support in understanding and managing illness over time. Focusing on endometriosis, an enigmatic chronic condition, we conducted interviews with specialists and focus groups with patients to elicit their work in care specifically pertaining to dealing with an enigmatic disease, both independently and in partnership, and how technology could support these efforts. We found that the work to care for the illness, including reflecting on the illness experience and planning for care, is significantly compounded by the complex nature of the disease: enigmatic condition means uncertainty and frustration in care and management; the multi-factorial and systemic features of endometriosis without any guidance to interpret them overwhelm patients and providers; the different temporal resolutions of this chronic condition confuse both patients and provides; and patients and providers negotiate medical knowledge and expertise in an attempt to align their perspectives. We note how this added complexity demands that patients and providers work together to find common ground and align perspectives, and propose three design opportunities (considerations to construct a holistic picture of the patient, design features to reflect and make sense of the illness, and opportunities and mechanisms to correct misalignments and plan for care) and implications to support patients and providers in their care work. Specifically, the enigmatic nature of endometriosis necessitates complementary approaches from human-centered computing and artificial intelligence, and thus opens a number of future research avenues.