Long intergenic noncoding RNAs (lincRNAs) play diverse regulatory roles in human development and disease, but little is known about their evolutionary history and constraint. Here, we characterize human lincRNA expression patterns in nine tissues across six mammalian species and multiple individuals. Of the 1898 human lincRNAs expressed in these tissues, we find orthologous transcripts for 80% in chimpanzee, 63% in rhesus, 39% in cow, 38% in mouse, and 35% in rat. Mammalian-expressed lincRNAs show remarkably strong conservation of tissue specificity, suggesting that it is selectively maintained. In contrast, abundant splice-site turnover suggests that exact splice sites are not critical. Relative to evolutionarily young lincRNAs, mammalian-expressed lincRNAs show higher primary sequence conservation in their promoters and exons, increased proximity to protein-coding genes enriched for tissue-specific functions, fewer repeat elements, and more frequent single-exon transcripts. Remarkably, we find that ∼20% of human lincRNAs are not expressed beyond chimpanzee and are undetectable even in rhesus. These hominid-specific lincRNAs are more tissue specific, enriched for testis, and faster evolving within the human lineage.