Recent reports suggest that 10 to 30% of severe acute respiratory syndrome coronavirus 2 (SARS- CoV-2) infected patients are asymptomatic and that viral shedding may occur before symptom onset. Therefore, there is an urgent need to increase diagnostic testing capabilities to prevent disease spread. We developed P-BEST, a method for Pooling-Based Efficient SARS-CoV-2 Testing, which identifies all positive subjects within a set of samples using a single round of testing. Each sample is assigned into multiple pools using a combinatorial pooling strategy based on compressed sensing. We pooled sets of 384 samples into 48 pools, providing both an eightfold increase in testing efficiency and an eightfold reduction in test costs, while identifying up to five positive carriers. We then used P-BEST to screen 1115 health care workers using 144 tests. P- BEST provides an efficient and easy-to-implement solution for increasing testing capacity that can be easily integrated into diagnostic laboratories.