We sought to understand the dynamics of de novo resistant mutations arising during colistin treatment of an antibiotic-naive population of K. pneumoniae. We used a bioreactor model of infection and colistin treatment against the colistin susceptible K. pneumoniae Ecl8. Whole-genome sequencing and MIC profiling was used to characterize genetic and phenotypic state of the bacterial culture at three time points: before treatment, immediately after regrowth following challenge, and at the end point of the experiment. A mathematical model based on the birth-death process was used to gain further insights on the population dynamics of emerging resistant variants. We found that, after an initial decline, the population recovers within 24h due to the evolution of highly resistant clones which exhibit MICs over 100-fold higher than the parental strain. Recovery is caused by a small number of "founder cells" which have single point mutations mainly in the regulatory genes encoding crrB and pmrB. The mutants arise through spontaneous mutations prior to colistin treatment. We concluded that development of colistin resistance during treatment of K. pneumoniae infections is readily achieved if colistin is used as a monotherapy.