When a population of bacteria encounter a bactericidal antibiotic most cells die rapidly. However, a sub-population, known as "persister cells", can survive for prolonged periods in a non-growing, but viable, state. Persister cell frequency is dramatically increased by stresses such as nutrient deprivation, but it is unclear what pathways are required to maintain viability, and how this process is regulated. To identify the genetic determinants of antibiotic persistence in mycobacteria, we carried out transposon mutagenesis high-throughput sequencing (Tn-Seq) screens in Mycobacterium abscessus (Mabs). This analysis identified genes essential in both spontaneous and stress-induced persister cells, allowing the first genetic comparison of these states in mycobacteria, and unexpectedly identified multiple genes involved in the detoxification of reactive oxygen species (ROS). We found that endogenous ROS were generated following antibiotic exposure, and that the KatG catalase-peroxidase contributed to survival in both spontaneous and starvation-induced persisters. We also found that that hypoxia significantly impaired bacterial killing, and notably, in the absence of oxygen, KatG became dispensable. Thus, the lethality of some antibiotics is amplified by toxic ROS accumulation, and persister cells depend on detoxification systems to remain viable.