Microorganisms are often studied as populations but the behaviour of single, individual cells can have important consequences. For example, tuberculosis, caused by the bacterial pathogen Mycobacterium tuberculosis, requires months of antibiotic therapy even though the bulk of the bacterial population dies rapidly. Shorter courses lead to high rates of relapse because subpopulations of bacilli can survive despite being genetically identical to those that are easily killed. In fact, mycobacteria create variability each time a cell divides, producing daughter cells with different sizes and growth rates. The mechanism(s) that underlie this high-frequency variation and how variability relates to survival of the population are unknown. Here we show that mycobacteria actively create heterogeneity. Using a fluorescent reporter and a fluorescence-activated cell sorting (FACS)-based transposon screen, we find that deletion of lamA, a gene of previously unknown function, decreases heterogeneity in the population by decreasing asymmetric polar growth. LamA has no known homologues in other organisms, but is highly conserved across mycobacterial species. We find that LamA is a member of the mycobacterial division complex (the 'divisome'). It inhibits growth at nascent new poles, creating asymmetry in polar growth. The kinetics of killing individual cells that lack lamA are more uniform and more rapid with rifampicin and drugs that target the cell wall. Our results show that mycobacteria encode a non-conserved protein that controls the pattern of cell growth, resulting in a population that is both heterogeneous and better able to survive antibiotic pressure.