The bacterial flagellum is a large extracellular protein organelle that extrudes from the cell surface. The flagellar filament is assembled from tens of thousands of flagellin subunits that are exported through the flagellar type III secretion system. Here, we measure the growth of Escherichia coli flagella in real time and find that, although the growth rate displays large variations at similar lengths, it decays on average as flagella lengthen. By tracking single flagella, we show that the large variations in growth rate occur as a result of frequent pauses. Furthermore, different flagella on the same cell show variable growth rates with correlation. Our observations are consistent with an injection-diffusion model, and we propose that an insufficient cytoplasmic flagellin supply is responsible for the pauses in flagellar growth in E. coli.