Chiral hypercycle replicators (first-order autocatalysis together with mutual cross-catalysis) formed from achiral or racemizing resources may lead to spontaneous mirror symmetry breaking (SMSB) without the need for additional heterochiral inhibition reactions, such as those of the Frank-like models, which are an obstacle for the emergence of evolutionary selection properties. The results indicate that the chemical models for the emergence of primordial autocatalytic self-reproducing systems, of and by themselves, can also explain naturally the emergence of biological homochirality.