Pseudomonas aeruginosa is a clinically significant pathogen that has alarming antibiotic resistance rates and very few candidate drugs in development. The challenges of novel drug discovery are exacerbated by incomplete knowledge of the essential genes across the species required for survival under infection conditions. We thus sought to define the core essential genome of P. aeruginosa by performing transposon insertion sequencing (Tn-Seq) on nine strains of P. aeruginosa isolated from different infection sites including wound, eye, lung, urinary tract, and blood, with an environmentally isolated strain for comparison, in five different media conditions: three were infection relevant media (serum, sputum, urine) and two were lab-based media (LB and M9 minimal). We developed a novel statistical model, FiTnEss, to classify genes as essential versus nonessential across all strain-media combinations. FiTnEss required minimal assumptions and had good predictive power in a limited set of validation studies with mutant strains of PA14 containing clean gene deletions. A core set of 321 essential genes emerged that are the highest probability targets for successful novel drug discovery against this important pathogen.