Caregivers mediate children's access to HIV care and their adherence to treatment. Support for caregivers may improve health outcomes in children, but fear of HIV stigma and discrimination can affect both uptake and delivery of support services. Within a trial evaluating community-based support for caregivers of newly HIV diagnosed children in Harare, Zimbabwe, we conducted a longitudinal qualitative study to explore how stigma affected delivery and acceptance of the intervention. We conducted semi-structured interviews with 36 caregivers, 15 children, and 20 community health workers (CHWs). Children and caregivers described experiencing or witnessing stigma and discrimination, causing some to resist home visits by CHWs. Anxiety around stigma made it difficult for CHWs to promote key messages. In response, CHWs adapted the intervention by meeting caregivers outside the home, pretending to be friends or relatives, and proactively counteracting stigmatising beliefs. As members of local communities, some CHWs shared concerns about discrimination. HIV stigma can hinder "getting a foot over the threshold" in community-based programmes, particularly for households most affected by discrimination and thus least likely to engage with services. For community support programmes to be effective, stigma-related resistance should be addressed from the outset, including CHWs' own concerns regarding HIV stigma.