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Wildfires are becoming more frequent in parts of the globe, but predicting where and when wildfires occur remains difficult. To predict wildfire extremes across the contiguous United States, we integrate a 30‐yr wildfire record with meteorological and housing data in spatiotemporal Bayesian statistical models with spatially varying nonlinear effects. We compared different distributions for the number and sizes of large fires to generate a posterior predictive distribution based on finite sample maxima for extreme events (the largest fires over bounded spatiotemporal domains). A zero‐inflated negative binomial model for fire counts and a lognormal model for burned areas provided the best performance. This model attains 99% interval coverage for the number of fires and 93% coverage for fire sizes over a six year withheld data set. Dryness and air temperature strongly predict extreme wildfire probabilities. Housing density has a hump‐shaped relationship with fire occurrence, with more fires occurring at intermediate housing densities. Statistically, these drivers affect the chance of an extreme wildfire in two ways: by altering fire size distributions, and by altering fire frequency, which influences sampling from the tails of fire size distributions. We conclude that recent extremes should not be surprising, and that the contiguous United States may be on the verge of even larger wildfire extremes. [ABSTRACT FROM AUTHOR]