Two fundamental properties of animate matter, specific complexity and purposeful organization (teleonomy), are traced to their origin, applying Eigen's theory of self-organization of matter. Template-replicating copolymers possess the three dynamic properties that are essential for prebiotic evolution: autocatalysis, diversification and selection. By autocatalysis, even a single microscopic molecule replicates exponentially to macroscopic quantities. By diversification, it extends to a divergent distribution of such molecules. By selection, the distribution converges to a 'quasi-species' that possesses properties like 'survival' and 'adaptation' to its environment. These are teleonomic properties that evolved from a nonteleonomic distribution by selection. Alternating divergent and convergent courses of chemical evolution lead such distributions to ever-growing complexity, including mutual catalytic interactions between the template-replicating copolymers and their chemical environment. Thus, chemical evolution may have started from even a single step, a de novo synthesis of a template-replicating copolymer, and arrived at a primordial living cell, just as biological evolution has started from a primordial cell and arrived at the biological world of today.