Nucleation is a fundamental step in atmospheric new-particle formation. However, laboratory experiments on nucleation have systematically failed to demonstrate sulfuric acid particle formation rates as high as those necessary to account for ambient atmospheric concentrations, and the role of sulfuric acid in atmospheric nucleation has remained a mystery. Here, we report measurements of new particles (with diameters of approximately 1.5 nanometers) observed immediately after their formation at atmospherically relevant sulfuric acid concentrations. Furthermore, we show that correlations between measured nucleation rates and sulfuric acid concentrations suggest that freshly formed particles contain one to two sulfuric acid molecules, a number consistent with assumptions that are based on atmospheric observations. Incorporation of these findings into global models should improve the understanding of the impact of secondary particle formation on climate.