During the bacterial cell cycle, chromosome replication and cell division must be coordinated with overall cell growth in order to maintain the correct ploidy and cell size. The spatial and temporal coordination of these processes in mycobacteria is not understood. Here we use microfluidics and time-lapse fluorescence microscopy to measure the dynamics of cell growth, division and chromosome replication in single cells of Mycobacterium smegmatis. We find that single-cell growth is size-dependent (large cells grow faster than small cells), which implicates a size-control mechanism in cell-size homoeostasis. Asymmetric division of mother cells gives rise to unequally sized sibling cells that grow at different velocities but show no differential sensitivity to antibiotics. Individual cells are restricted to one round of chromosome replication per cell division cycle, although replication usually initiates in the mother cell before cytokinesis and terminates in the daughter cells after cytokinesis. These studies reveal important differences between cell cycle organization in mycobacteria compared with better-studied model organisms.