A major challenge in studying tumor cell invasion into its surrounding tissue is to identify the contribution of individual factors in the tumor microenvironment (TME) to the process. One of the important elements of the TME is the fibrous extracellular matrix (ECM) which is known to influence cancer cell invasion, but exactly how remains unclear. Therefore, there is a need for new models to unravel mechanisms behind the tumor-ECM interaction. In this article, we present a new microfabrication method, called selective curing, to integrate ECM-mimicking layers between two microfluidic channels. This method enables us to study the effect of 3D matrices with controlled architecture, beyond the conventionally used hydrogels, on cancer invasion in a controlled environment. As a proof of principle, we have integrated two electrospun Polycaprolactone (PCL) matrices with different fiber diameters in one chip. We then studied the 3D migration of MDA-MB-231 breast cancer cells into the matrices under the influence of a chemotactic gradient. The results show that neither the invasion distance nor the general cell morphology is affected significantly by the difference in fiber size of these matrices. The cells however do produce longer and more protrusions in the matrix with smaller fiber size. This microfluidic system enables us to study the influence of other factors in the TME on cancer development as well as other biological applications as it provides a controlled compartmentalized environment compatible with cell culturing.