While there are both ethical and practical imperatives to address health inequity issues related to chronic disease management for persons with social complexity, existing programs often do not appropriately address the needs of these individuals. This leads to low levels of participation in programs, suboptimal chronic disease management, and higher health-care utilization. The aims of this project were to describe the challenges related to availability, accessibility, and acceptability faced by socially complex patients with Chronic Obstructive Pulmonary Disease (COPD) who were eligible, but declined enrollment in a traditional Chronic Disease Management Program (CDMP). Using a qualitative descriptive study approach informed by a health equity lens, interviews with participants, managers, and a focus group with providers were used to gather data addressing the above aims. Qualitative data were analyzed using Braun and Clarke's theoretical thematic analysis approach. The ability of participants to manage chronic disease was profoundly influenced by contextual and personal factors, such as poverty, disability, personal attitudes and beliefs (including shame, mistrust, and hopelessness), and barriers inherent in the organization of the health-care system. The existing chronic disease management program did not adequately address the most critical needs of socially complex patients. Challenges with accessibility and acceptability of chronic disease management and health services played important roles in the ways these socially complex participants managed their chronic illness. The individualistic approach to self-management of chronic illness inherent in conventional CDMP can be poorly aligned with the needs, capacity, and circumstances of many socially complex patients. Innovative models of care that promote incremental and guided approaches to enhancing health and improving self-efficacy need further development and evaluation.