In this report, we describe the preparation and characterization of a new class of thermoset fibers with high elongation and elastic recovery. Integrating UV-activated thiol-ene photopolymerization and electrospinning, we demonstrate an environmentally friendly single step approach to convert small monomeric precursor molecules into highly elastic fibers and nonwoven mats. The fibers were derived by in situ photopolymerization of a trifunctional vinyl ether monomer and a tetrafunctional thiol. Although thermosets often offer good chemical and thermal stability, these fibers also have a high average elongation at break of 62%. The elastomeric nature of these vinyl-ether based fibers can be partly attributed to their subambient Tg and partly to the cross-link density, monomer structure, and resulting network homogeneity. Nonwoven mats of these fibers were also stretchable and exhibited a much higher elongation at break of about 85%. These thermoset stretchable fibers could have potential applications as textile, biomedical, hot chemical filtration, and composite materials.