Eukaryotic cells under stress repress translation and localize these messenger RNAs (mRNAs) to cytoplasmic RNA granules. We show that specific stress stimuli induce the assembly of RNA granules in an organelle with bacterial ancestry, the chloroplast of Chlamydomonas reinhardtii. These chloroplast stress granules (cpSGs) form during oxidative stress and disassemble during recovery from stress. Like mammalian stress granules, cpSGs contain poly(A)-binding protein and the small, but not the large, ribosomal subunit. In addition, mRNAs are in continuous flux between polysomes and cpSGs during stress. Localization of cpSGs within the pyrenoid reveals that this chloroplast compartment functions in this stress response. The large subunit of ribulosebisphosphate carboxylase/oxygenase also assembles into cpSGs and is known to bind mRNAs during oxidative stress, raising the possibility that it plays a role in cpSG assembly. This discovery within such an organelle suggests that mRNA localization to granules during stress is a more general phenomenon than currently realized.