Chronic Lymphocytic Leukemia (CLL) is a heterogeneous disease associated with diverse clinical and molecular profiles, suggesting long-term clonal evolution driven by genetic diversification from a small, often undetected, subset of leukemic cells endowed with superior growth capacities. More importantly, this diversification process enhances the opportunity of CLL subclones to survive selective pressure, such as BTK or PLCG2 mutations that can abolish the effect of BTK inhibitors. While this evolutionary process is inevitable in leukemic cells, therapeutic intervention targeting the cells that have just replicated their DNA, and hence could have accumulated new genomic mutation, would be an effective strategy to significantly delay or abort the emergence of deleterious mutations.