Quorum sensing controls the expression of a wide range of important traits in the opportunistic pathogen Pseudomonas aeruginosa, including the expression of virulence genes and its CRISPR-cas immune system, which protects from bacteriophage (phage) infection. This finding has led to the speculation that synthetic quorum sensing inhibitors could be used to limit the evolution of CRISPR immunity during phage therapy. Here we use experimental evolution to explore if and how a quorum sensing inhibitor influences the population and evolutionary dynamics of P. aeruginosa upon phage DMS3vir infection. We find that chemical inhibition of quorum sensing decreases phage adsorption rates due to downregulation of the Type IV pilus, which causes delayed lysis of bacterial cultures and favours the evolution of CRISPR immunity. Our data therefore suggest that inhibiting quorum sensing may reduce rather than improve the therapeutic efficacy of pilus-specific phage, and this is likely a general feature when phage receptors are positively regulated by quorum sensing.