Leaf physiology determines the carbon acquisition of the whole plant, but there can be considerable variation in physiology and carbon acquisition within individual leaves. Alocasia macrorrhiza (L.) Schott is an herbaceous species that can develop very large leaves of up to 1 m in length. However, little is known about the hydraulic and photosynthetic design of such giant leaves. Based on previous studies of smaller leaves, and on the greater surface area for trait variation in large leaves, we hypothesized that A. macrorrhiza leaves would exhibit significant heterogeneity in structure and function. We found evidence of reduced hydraulic supply and demand in the outer leaf regions; leaf mass per area, chlorophyll concentration, and guard cell length decreased, as did stomatal conductance, net photosynthetic rate and quantum efficiency of photosystem II. This heterogeneity in physiology was opposite to that expected from a thinner boundary layer at the leaf edge, which would have led to greater rates of gas exchange. Leaf temperature was 8.8°C higher in the outer than in the central region in the afternoon, consistent with reduced stomatal conductance and transpiration caused by a hydraulic limitation to the outer lamina. The reduced stomatal conductance in the outer regions would explain the observed homogeneous distribution of leaf water potential across the leaf surface. These findings indicate substantial heterogeneity in gas exchange across the leaf surface in large leaves, greater than that reported for smaller-leafed species, though the observed structural differences across the lamina were within the range reported for smaller-leafed species. Future work will determine whether the challenge of transporting water to the outer regions can limit leaf size for plants experiencing drought, and whether the heterogeneity of function across the leaf surface represents a particular disadvantage for large simple leaves that might explain their global rarity, even in resource-rich environments.