Abstract
We analyse three moral dilemmas involving resource allocation in care for HIV-positive patients. Ole Norheim and Kjell Arne Johansson have argued that these cases reveal a tension between egalitarian concerns and concerns for better population health. We argue, by contrast, that these cases reveal a tension between, on the one hand, a concern for equal *chances*, and, on the other hand, both a concern for better health and an egalitarian concern for equal *outcomes*. We conclude that, in these cases, there is much less tension than Norheim and Johansson claim between egalitarian concerns and concerns for better population health.