The mechanism by which enzymes arose from both abiotic and biological worlds remains an unsolved natural mystery. We postulate that an enzyme can emerge from any sequence of any functional polymer under permissive evolutionary conditions. To support this premise, we have arbitrarily chosen a 50-nucleotide DNA fragment encoding for the Bos taurus (cattle) albumin mRNA and subjected it to test-tube evolution to derive a catalytic DNA (DNAzyme) with RNA-cleavage activity. After only a few weeks, a DNAzyme with significant catalytic activity has surfaced. Sequence comparison reveals that seven nucleotides are responsible for the conversion of the noncatalytic sequence into the enzyme. Deep sequencing analysis of DNA pools along the evolution trajectory has identified individual mutations as the progressive drivers of the molecular evolution. Our findings demonstrate that an enzyme can indeed arise from a sequence of a functional polymer via permissive molecular evolution, a mechanism that may have been exploited by nature for the creation of the enormous repertoire of enzymes in the biological world today.