Environments such as the ocean, the soil, and the human body support tremendous microbial diversity. Uncovering the mechanisms by which a large number of microbial species can coexist on limited resources remains an important open problem. Here I will discuss this problem in unique context: bacteria that inhabit tumors. Bacterial colonization of solid tumors is widespread, but how the tumor environment affects bacterial growth (and vice versa) is poorly understood. Our experimental collaborators infect mouse tumors with DNA-barcoded bacteria, creating competition among thousands of clonal bacterial "species". We find that after an initial expansion period, clone sizes exhibit universal power-law statistics. These statistics are robust across experiments and collection times, and unique to bacteria grown in the tumor environment rather than in liquid culture. Combining population ecology with nonequilibrium statistical physics, we develop a mechanistic theory of intra-tumor bacterial growth that includes an infection bottleneck, local growth constraints, global resource competition, and environmental noise. Our simple physical theory captures the dynamics and the statistics of the experiments, explains the uniqueness of the observations to the tumor environment, and represents an important step in quantitatively characterizing the tumor microbiome.