The prevalent presence of a single chiral variant of molecules in live organisms is one of the most distinctive signs of life as a global phenomenon. One of the greatest ambitions of biochemistry and astrobiology is to provide an explanation of this predominance. Several mechanisms were proposed in the past, from the propagation of chirality from a homo-chiral substrate to the amplification of effects associated with electro-weak interactions. Here, a different scenario is proposed: anomalous fluctuations associated with a self-replication scenario can lead to the selective extinction of primordial organisms using one of two enantiomers as an enzyme. These fluctuations arise spontaneously under very general conditions. The idea is based on three key points: (a) the simulation of early biological processes as a ‘board game’; (b) the presence of large fluctuations during an autocatalytic process; (c) the presence of a limited source of chemical energy, inducing a form of competition in a primordial replicator population. In order to demonstrate this mechanism, a computational model is developed, describing the ‘struggle for life’ of two different kinds of primordial replicators on a ‘chessboard’ with periodic boundary conditions; each replicator employs enzymes of different chirality on a non-chiral substrate, thereby with no selective advantage. The replication occurs randomly and with a fixed probability, providing that a sufficient amount of chemical energy is locally available. For the first time, our model includes the local balance of chemical energy in a molecular form on the substrate. The correlation between the chemical energy and the local populations is shown. Results clearly show that strong fluctuations in the number of individuals of each species and subsequent selective extinction events of one of the two species are observed. These studies may contribute to shed light on the most mysterious phase transition that occurred during the biochemical evolution of our planet.