Background: Australian federal and jurisdictional governments are implementing ambitious policy initiatives intended to improve health care access and outcomes for Aboriginal and Torres Strait Islander people. In this qualitative study we explored Aboriginal Medical Service (AMS) staff views on factors needed to improve chronic care systems and assessed their relevance to the new policy environment. Methods. Two theories informed the study: (1) 'candidacy', which explores "the ways in which people's eligibility for care is jointly negotiated between individuals and health services"; and (2) kanyini or 'holding', a Central Australian philosophy which describes the principle and obligations of nurturing and protecting others. A structured health systems assessment, locally adapted from Chronic Care Model domains, was administered via group interviews with 37 health staff in six AMSs and one government Indigenous-led health service. Data were thematically analysed. Results: Staff emphasised AMS health care was different to private general practices. Consistent with kanyini, community governance and leadership, community representation among staff, and commitment to community development were important organisational features to retain and nurture both staff and patients. This was undermined, however, by constant fear of government funding for AMSs being withheld. Staff resourcing, information systems and high-level leadership were perceived to be key drivers of health care quality. On-site specialist services, managed by AMS staff, were considered an enabling strategy to increase specialist access. Candidacy theory suggests the above factors influence whether a service is 'tractable' and 'navigable' to its users. Staff also described entrenched patient discrimination in hospitals and the need to expend considerable effort to reinstate care. This suggests that Aboriginal and Torres Strait Islander people are still constructed as 'non-ideal users' and are denied from being 'held' by hospital staff. Conclusions: Some new policy initiatives (workforce capacity strengthening, improving chronic care delivery systems and increasing specialist access) have potential to address barriers highlighted in this study. Few of these initiatives, however, capitalise on the unique mechanisms by which AMSs 'hold' their users and enhance their candidacy to health care. Kanyini and candidacy are promising and complementary theories for conceptualising health care access and provide a potential framework for improving systems of care.