"Treat-all" programmes aim to improve clinical outcomes and to reduce HIV transmission through regular HIV testing and immediate offer of antiretroviral therapy (ART) for those diagnosed HIV-positive, irrespective of immunological status and symptoms of disease. Global narratives on the benefits of Treat-all anticipate reduced HIV-related stigma and increased "normalisation" of HIV with Treat-all implementation, whereby HIV is remoulded as a manageable, chronic condition where stigmatising symptoms can be concealed. Drawing on Goffman's stigma work, we aimed to investigate how stigma may influence the engagement of clinically asymptomatic people living with HIV (PLHIV) with Treat-all HIV care in Shiselweni, Eswatini (formerly Swaziland). This longitudinal research comprised 106 interviews conducted from August 2016 to September 2017, including repeated interviews with 30 PLHIV, and one-off interviews with 20 healthcare workers. Data were analysed thematically using NVivo 11, drawing upon principles of grounded theory to generate findings inductively from participants' accounts. Stigma was pervasive within the narratives of PLHIV, framing their engagement with treatment and care. Many asymptomatic PLHIV were motivated to initiate ART in order to maintain a "discreditable" status, by preventing the development of visible and exposing symptoms. However, engagement with treatment and care services could itself be exposing. PLHIV described the ways in which these "invisibilising" benefits and exposing risks of ART were continually assessed and navigated over time. Where the risk of exposure was deemed too great, this could lead to intermittent treatment-taking, and disengagement from care. Addressing HIV related stigma is crucial to the success of Treat-all, and should thus be a core component of HIV responses.