Amino acids were most likely available on the primitive Earth, produced in the primitive atmosphere or in hydrothermal vents. Import of extraterrestrial amino acids may have represented the major supply, as suggested by micrometeorite collections and simulation experiments in space and in the laboratory. Selective condensation of amino acids in water has been achieved via N-carboxy anydrides. Homochiral peptides with an alternating sequence of hydrophobic and hydrophilic amino acids adopt stereoselective and thermostable beta-pleated sheet structures. Some of the homochiral beta-sheets strongly accelerate the hydrolysis of oligoribonucleotides. The beta-sheet-forming peptides have also been shown to protect their amino acids from racemization. Even if peptides are not able to self-replicate, i.e., to replicate a complete sequence from the mixture of amino acids, the accumulation of chemically active peptides on the primitive Earth appears plausible via thermostable and stereoselective beta-sheets made of alternating sequences.