Achieving global food security for the estimated 9 billion people by 2050 is a major scientific challenge. Crop productivity is fundamentally restricted by the rate of fixation of atmospheric carbon. The dedicated enzyme, RubisCO, has a low turnover and poor specificity for CO2. This limitation of C3 photosynthesis (the basic carbon-assimilation pathway present in all plants) is alleviated in some lineages by use of carbon-concentrating-mechanisms, such as the C4 cycle-a biochemical pump that concentrates CO2 near RubisCO increasing assimilation efficacy. Most crops use only C3 photosynthesis, so one promising research strategy to boost their productivity focuses on introducing a C4 cycle. The simplest proposal is to use the cycle to concentrate CO2 inside individual chloroplasts. The photosynthetic efficiency would then depend on the leakage of CO2 out of a chloroplast. We examine this proposal with a 3D spatial model of carbon and oxygen diffusion and C4 photosynthetic biochemistry inside a typical C3-plant mesophyll cell geometry. We find that the cost-efficiency of C4 photosynthesis depends on the gas permeability of the chloroplast envelope, the C4 pathway having higher quantum efficiency than C3 for permeabilities below 300 xcexbcm/s. However, at higher permeabilities the C4 pathway still provides a substantial boost to carbon assimilation with only a moderate decrease in efficiency. The gains would be capped by the ability of chloroplasts to harvest light, but even under realistic light regimes a 100% boost to carbon assimilation is possible. This could be achieved in conjunction with lower investment in chloroplasts if their cell surface coverage is also reduced. Incorporation of this C4 cycle into C3 crops could thus promote higher growth rates and better drought resistance in dry, high-sunlight climates.