Conventional cell culture remains the most frequently used preclinical model, despite its proven limited ability to predict clinical results in cancer. Microfluidic cancer-on-chip models have been proposed to bridge the gap between the oversimplified conventional 2D cultures and more complicated animal models, which have limited ability to produce reliable and reproducible quantitative results. Here, we present a microfluidic cancer-on-chip model that reproduces key components of a complex tumor microenvironment in a comprehensive manner, yet is simple enough to provide robust quantitative descriptions of cancer dynamics. This microfluidic cancer-on-chip model, the "Evolution Accelerator," breaks down a large population of cancer cells into an interconnected array of tumor microenvironments while generating a heterogeneous chemotherapeutic stress landscape. The progression and the evolutionary dynamics of cancer in response to drug gradient can be monitored for weeks in real time, and numerous downstream experiments can be performed complementary to the time-lapse images taken through the course of the experiments.