Despite the increasing number of effective anti-cancer therapies, successful treatment is limited by the development of drug resistance. While the contribution of genetic factors to drug resistance is undeniable, little is known about how drug-sensitive cells first evade drug action to proliferate in drug. Using our new cell-tracking pipeline called EllipTrack, we tracked the response of thousands of single melanoma cells to BRAF inhibitors and show that a subset of cells escapes drug within the first 3 days of treatment. These escapees cycle periodically in drug and out-proliferate non-escapees over extended treatment. Cell-cycle re-entry occurs via a nongenetic mechanism involving activation of ATF4, validated in ex vivo cultures of patient biopsies. Furthermore, escapees experience incomplete licensing of replication origins, leading to heightened DNA replication stress and DNA damage. Our work reveals a mutagenesis-prone, expanding subpopulation of early drug escapees that may represent a reservoir for the development of
permanent drug resistance.