Developing countries are vulnerable to the adverse effects of climate change, yet there is disagreement about what they should do to protect themselves from anticipated damages. In particular, it is unclear what the optimal balance is between investments in traditional productive capital (which increases output but is vulnerable to climate change), and investments in adaptive capital (which is unproductive in the absence of climate change but ‘climate-proofs’ vulnerable capital). We develop a model of investment in adaptive and productive capital stocks, and show that while it is unlikely that the optimal strategy involves no adaptation, the scale and composition of optimal investments depends on empirical context. Application of our model to sub-Saharan Africa suggests, however, that in most contingencies it will be optimal to grow the adaptive sector more rapidly than the vulnerable sector over the coming decades, although it never exceeds 1 per cent of the economy. Our sensitivity analysis goes well beyond the existing literature in evaluating the robustness of this finding.