In the present work, we demonstrate the ability to electrospin wheat gluten, a polydisperse plant protein polymer that is currently available at roughly $0.50/lb. A variety of electrospinning experiments were carried out with wheat gluten from two sources, at different solution concentrations, and with native and denatured wheat gluten to illustrate the interplay between protein structure and the fluid dynamics of the electrospinning process. The presence of both cylindrical and flat fibers was observed in the nonwoven mats, which were characterized using both polarized optical microscopy and field emission scanning electron microscopy. Retardance images obtained by polarized optical microscopy exhibited evidence of molecular orientation at the surface of the fibers. We believe that fiber formation by electrospinning is a result of both chain entanglements and the presence of reversible junctions in the protein, in particular, the breaking and reforming of disulfide bonds that occur via a thiol/disulfide interchange reaction. The presence of the highest molecular weight glutenin polymer chains in the wheat protein appeared to be responsible for the lower threshold concentration for fiber formation, relative to that of a lower molecular weight fraction of wheat protein devoid of the high molecular weight glutenin component. Denaturation of the wheat protein, however, clearly disrupted this delicate balance of properties in the experimental regimes we investigated, as electrospun fibers from the denatured state were not observed.