We propose that chemical evolution can take place by natural selection if a geophysical process is capable of heterotrophic formation of liposomes that grow at some base rate, divide by external agitation, and are subject to stochastic chemical avalanches, in the absence of nucleotides or any monomers capable of modular heredity. We model this process using a simple hill-climbing algorithm, and an artificial chemistry that is unique in exhibiting conservation of mass and energy in an open thermodynamic system. Selection at the liposome level results in the stabilization of rarely occurring molecular autocatalysts that either catalyse or are consumed in reactions that confer liposome level fitness; typically they contribute in parallel to an increasingly conserved intermediary metabolism. Loss of competing autocatalysts can sometimes be adaptive. Steady-state energy flux by the individual increases due to the energetic demands of growth, but also of memory, i.e. maintaining variations in the chemical network. Self-organizing principles such as those proposed by Kauffman, Fontana, and Morowitz have been hypothesized as an ordering principle in chemical evolution, rather than chemical evolution by natural selection. We reject those notions as either logically flawed or at best insufficient in the absence of natural selection. Finally, a finite population model without elitism shows the practical evolutionary constraints for achieving chemical evolution by natural selection in the lab.