Diffusion limited aggregation (DLA) is a random growth model which was originally introduced in 1981 by Witten and Sander. This model is prevalent in nature and has many applications in the physical sciences as well as industrial processes. We consider a simplified version of DLA known as the Hastings-Levitov HL(0) model, and show that under certain scaling conditions this model gives rise to a limit object known as the Brownian web.