The self-assembly of peptide and protein molecules into nanoscale filaments is a process associated with both biological function and malfunction. Microfluidic techniques can provide powerful tools in the study of such aggregation phenomena while providing access to exploring the role of molecular interactions in disease development. Yet, a common challenge encountered in the study of protein aggregation is the difficulty in achieving spatial and temporal control of the underlying processes. Here, we present a planar (2-D) device allowing for both the generation and confinement of 10 000 monodisperse water-in-oil droplets in an array of chambers with a trapping efficiency of 99%. Due to the specific geometry of the device, droplets can be formed and immediately trapped on the same chip, without the need for continuous flow of the oil phase. Furthermore, we demonstrate the capability of this device as a platform to study the aggregation kinetics and determine stochastic molecular nanoscale self-assembly events in a highly parallel manner for the aggregation of the dipeptide, diphenylalanine, the core recognition motif of the Aβ-42 peptide associated with Alzheimer's disease. The ability to reproducibly generate and confine monodisperse water-in-oil droplets with an extremely high trapping efficiency while maintaining entrapment under zero-flow conditions, on timescales compatible with observing molecular self-assembly events, renders it promising for numerous potential further applications in the biological and biophysical fields.