Tuning the electronic properties of a material by subjecting it to strain constitutes an important strategy to enhance the performance of semiconducting electronic devices. Using local strain, confinement potentials for excitons can be engineered, with exciting possibilities for trapping excitons for quantum optics and for efficient collection of solar energy. Two-dimensional materials are able to withstand large strains before rupture, offering a unique opportunity to introduce large local strains. Here, we study atomically thin MoS2 layers with large local strains of up to 2.5% induced by controlled delamination from a substrate. Using simultaneous scanning Raman and photoluminescence imaging, we spatially resolve a direct bandgap reduction of up to 90 meV induced by local strain. We observe a funnel effect in which excitons drift hundreds of nanometers to lower bandgap regions before recombining, demonstrating exciton confinement by local strain. The observations are supported by an atomistic tight-binding model developed to predict the effect of inhomogeneous strain on the local electronic states in MoS2. The possibility of generating large strain-induced variations in exciton trapping potentials opens the door for a variety of applications in atomically thin materials including photovoltaics, quantum optics and two-dimensional optoelectronic devices.

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