A key challenge for origin of life research is understanding how the homochirality of extant biological systems may have emerged during the abiotic phase of chemical evolution. Living systems depend on bio-macromolecules made from chiral building blocks and a crucial question is the relationship of polymerization with the emergence of homochirality. We present a reaction scheme demonstrating how spontaneous mirror symmetry breaking (SMSB) can be achieved in enantioselective polymerization without chiral inhibition and without autocatalysis. The model is based on nucleated cooperative polymerization: nucleation, elongation, dissociation, fusion and fragmentation and monomer racemization. These are micro-reversible processes subject to constraints dictated by chemical thermodynamics. To maintain this closed system out of equilibrium, we model an external energy source which induces the irreversible breakage of the longest polymers in the system. Simulations reveal that SMSB can be achieved starting from the tiny intrinsic statistical fluctuations about the idealized mirror symmetric composition.