||Proteins are translated from the N- to the C-terminal, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the protein data bank (PDB). We find remarkable enrichment of α-helices at the C terminal and β-sheets at the N terminal. Furthermore, this α-β asymmetry correlates with sequence length and contact order, both known determinants of folding rate. Hence, we propose and examine the `slowest-first' scheme, whereby protein sequences evolved structural asymmetry to accelerate co-translational folding (CTF): the slowest-folding elements (e.g. β-sheets) are positioned near the N terminal so they have more time to fold during translation. We predict that CTF can be accelerated, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB reveals that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in sequence asymmetry.