Repetitive proteins are thought to have arisen through the amplification of subdomain-sized peptides. Many of these originated in a non-repetitive context as cofactors of RNA-based replication and catalysis, and required the RNA to assume their active conformation. In search of the origins of one of the most widespread repeat protein families, the tetratricopeptide repeat (TPR), we identified several potential homologs of its repeated helical hairpin in non-repetitive proteins, including the putatively ancient ribosomal protein S20 (RPS20), which only becomes structured in the context of the ribosome. We evaluated the ability of the RPS20 hairpin to form a TPR fold by amplification and obtained structures identical to natural TPRs for variants with 2-5 point mutations per repeat. The mutations were neutral in the parent organism, suggesting that they could have been sampled in the course of evolution. TPRs could thus have plausibly arisen by amplification from an ancestral helical hairpin.