In most organisms, the heat-shock response involves increased heat-shock gene transcription. In Kinetoplastid protists, however, virtually all control of gene expression is post-transcriptional. Correspondingly, Trypanosoma brucei heat-shock protein 70 (HSP70) synthesis after heat shock depends on regulation of HSP70 mRNA turnover. We here show that the T. brucei CCCH zinc finger protein ZC3H11 is a post-transcriptional regulator of trypanosome chaperone mRNAs. ZC3H11 is essential in bloodstream-form trypanosomes and for recovery of insect-form trypanosomes from heat shock. ZC3H11 binds to mRNAs encoding heat-shock protein homologues, with clear specificity for the subset of trypanosome chaperones that is required for protein refolding. In procyclic forms, ZC3H11 was required for stabilisation of target chaperone-encoding mRNAs after heat shock, and the HSP70 mRNA was also decreased upon ZC3H11 depletion in bloodstream forms. Many mRNAs bound to ZC3H11 have a consensus AUU repeat motif in the 3'-untranslated region. ZC3H11 bound preferentially to AUU repeats in vitro, and ZC3H11 regulation of HSP70 mRNA in bloodstream forms depended on its AUU repeat region. Tethering of ZC3H11 to a reporter mRNA increased reporter expression, showing that it is capable of actively stabilizing an mRNA. These results show that expression of trypanosome heat-shock genes is controlled by a specific RNA-protein interaction. They also show that heat-shock-induced chaperone expression in procyclic trypanosome enhances parasite survival at elevated temperatures.