Many photosynthetic organisms enhance the performance of their CO2-fixing enzyme Rubisco by operating a CO2-concentrating mechanism (CCM). Most CCMs in eukaryotic algae supply concentrated CO2 to Rubisco in an organelle called the pyrenoid. Ongoing efforts seek to engineer an algal CCM into crops that lack a CCM to increase yields. To advance our basic understanding of the algal CCM, we develop a chloroplast-scale reaction-diffusion model to analyze the efficacy and the energy efficiency of the CCM in the green alga Chlamydomonas reinhardtii. We show that achieving an effective and energetically efficient CCM requires a physical barrier such as thylakoid stacks or a starch sheath to reduce CO2 leakage out of the pyrenoid matrix. Our model provides insights into the relative performance of two distinct inorganic carbon uptake strategies: at air-level CO2, a CCM can operate effectively by taking up passively diffusing external CO2 and catalyzing its conversion to HCO3-, which is then trapped in the chloroplast; however, at lower external CO2 levels, effective CO2 concentration requires active import of HCO3-. We also find that proper localization of carbonic anhydrases can reduce futile carbon cycling between CO2 and HCO3-, thus enhancing CCM performance. We propose a four-step engineering path that increases predicted CO2 saturation of Rubisco up to seven-fold at a theoretical cost of only 1.5 ATP per CO2 fixed. Our system-level analysis establishes biophysical principles underlying the CCM that are broadly applicable to other algae and provides a framework to guide efforts to engineer an algal CCM into land plants.