PURPOSE: The population and spatial characteristics of COVID-19 infections are poorly understood, but there is increasing evidence that in addition to individual clinical factors, demographic, socioeconomic, and racial characteristics play an important role. METHODS: We analyzed positive COVID-19 testing results counts within New York City ZIP Code Tabulation Areas with Bayesian hierarchical Poisson spatial models using integrated nested Laplace approximations. RESULTS: Spatial clustering accounted for approximately 32% of the variation in the data. There was a nearly five-fold increase in the risk of a positive COVID-19 test (incidence density ratio = 4.8, 95% credible interval 2.4, 9.7) associated with the proportion of black/African American residents. Increases in the proportion of residents older than 65 years, housing density, and the proportion of residents with heart disease were each associated with an approximate doubling of risk. In a multivariable model including estimates for age, chronic obstructive pulmonary disease, heart disease, housing density, and black/African American race, the only variables that remained associated with positive COVID-19 testing with a probability greater than chance were the proportion of black/African American residents and proportion of older persons. CONCLUSIONS: Areas with large proportions of black/African American residents are at markedly higher risk that is not fully explained by characteristics of the environment and pre-existing conditions in the population.