Phages impose strong selection on bacteria to evolve resistance against viral predation. Bacteria can rapidly evolve phage resistance via receptor mutation or using their CRISPR-Cas adaptive immune systems. Acquisition of CRISPR immunity relies on the insertion of a phage-derived sequence into CRISPR arrays in the bacterial genome. Using Pseudomonas aeruginosa and its phage DMS3vir as a model, we demonstrate that conditions that reduce bacterial growth rates, such as exposure to bacteriostatic antibiotics (which inhibit cell growth without killing), promote the evolution of CRISPR immunity. We demonstrate that this is due to slower phage development under these conditions, which provides more time for cells to acquire phage-derived sequences and mount an immune response. Our data reveal that the speed of phage development is a key determinant of the evolution of CRISPR immunity and suggest that use of bacteriostatic antibiotics can trigger elevated levels of CRISPR immunity in human-associated and natural environments.