COVID-19 vaccines have been authorized in multiple countries and more are under rapid development. Careful design of a vaccine prioritization strategy across socio-demographic groups is a crucial public policy challenge given that (1) vaccine supply will be constrained for the first several months of the vaccination campaign, (2) there are stark differences in transmission and severity of impacts from SARS-CoV-2 across groups, and (3) SARS-CoV-2 differs markedly from previous pandemic viruses. We assess the optimal allocation of a limited vaccine supply in the U.S. across groups differentiated by age and also essential worker status, which constrains opportunities for social distancing. We model transmission dynamics using a compartmental model parameterized to capture current understanding of the epidemiological characteristics of COVID-19, including key sources of group heterogeneity (susceptibility, severity, and contact rates). We investigate three alternative policy objectives (minimizing infections, years of life lost, or deaths) and model a dynamic strategy that evolves with the population epidemiological status. We find that this temporal flexibility contributes substantially to public health goals. Older essential workers are typically targeted first. However, depending on the objective, younger essential workers are prioritized to control spread or seniors to directly control mortality. When the objective is minimizing deaths, relative to an untargeted approach, prioritization averts deaths on a range between 20,000 (when non-pharmaceutical interventions are strong) and 300,000 (when these interventions are weak). We illustrate how optimal prioritization is sensitive to several factors, most notably vaccine effectiveness and supply, rate of transmission, and the magnitude of initial infections.