Diurnal gene expression patterns underlie time-of-the-day–specific functional specialization of tissues. However, available circadian gene expression atlases of a few organs are largely from nocturnal vertebrates. We report the diurnal transcriptome of 64 tissues, including 22 brain regions, sampled every 2 hours over 24 hours, from the primate Papio anubis (baboon). Genomic transcription was highly rhythmic, with up to 81.7% of protein-coding genes showing daily rhythms in expression. In addition to tissue-specific gene expression, the rhythmic transcriptome imparts another layer of functional specialization. Most ubiquitously expressed genes that participate in essential cellular functions exhibit rhythmic expression in a tissue-specific manner. The peak phases of rhythmic gene expression clustered around dawn and dusk, with a “quiescent period” during early night. Our findings also unveil a different temporal organization of central and peripheral tissues between diurnal and nocturnal animals.