Persistent infections are frequently caused by dormant and biofilm-associated bacteria, which often display characteristically slow growth. Antibiotics that require rapid cell growth may be ineffective against these organisms and thus fail to prevent reoccurring infections. In contrast to growth-based antimicrobial agents, membrane-targeting drugs effectively kill slow-growing bacteria. Herein we introduce 2-((3-(3,6-dichloro-9H-carbazol-9-yl)-2-hydroxypropyl)amino)-2-(hydroxymethyl)propane-1,3-diol (DCAP), a potent broad-spectrum antibiotic that reduces the transmembrane potential of Gram-positive and Gram-negative bacteria and causes mislocalization of essential membrane-associated proteins, including MinD and FtsA. Importantly, DCAP kills nutrient-deprived microbes and sterilizes bacterial biofilms. DCAP is lethal against bacterial cells, has no effect on red blood cell membranes, and only decreases the viability of mammalian cells after ≥6 h. We conclude that membrane-active compounds are a promising solution for treating persistent infections. DCAP expands the limited number of compounds in this class of therapeutic small molecules and provides new opportunities for the development of potent broad-spectrum antimicrobial agents.