Biological carbon fixation is a key step in the global carbon cycle that regulates the atmosphere's composition while producing the food we eat and the fuels we burn. Approximately one-third of global carbon fixation occurs in an overlooked algal organelle called the pyrenoid. The pyrenoid contains the CO2-fixing enzyme Rubisco and enhances carbon fixation by supplying Rubisco with a high concentration of CO2 Since the discovery of the pyrenoid more that 130 y ago, the molecular structure and biogenesis of this ecologically fundamental organelle have remained enigmatic. Here we use the model green alga Chlamydomonas reinhardtii to discover that a low-complexity repeat protein, Essential Pyrenoid Component 1 (EPYC1), links Rubisco to form the pyrenoid. We find that EPYC1 is of comparable abundance to Rubisco and colocalizes with Rubisco throughout the pyrenoid. We show that EPYC1 is essential for normal pyrenoid size, number, morphology, Rubisco content, and efficient carbon fixation at low CO2 We explain the central role of EPYC1 in pyrenoid biogenesis by the finding that EPYC1 binds Rubisco to form the pyrenoid matrix. We propose two models in which EPYC1's four repeats could produce the observed lattice arrangement of Rubisco in the Chlamydomonas pyrenoid. Our results suggest a surprisingly simple molecular mechanism for how Rubisco can be packaged to form the pyrenoid matrix, potentially explaining how Rubisco packaging into a pyrenoid could have evolved across a broad range of photosynthetic eukaryotes through convergent evolution. In addition, our findings represent a key step toward engineering a pyrenoid into crops to enhance their carbon fixation efficiency.