We present the results of a search for the production of an excited state of the electron, e*, in proton-antiproton collisions at sqrt(s) = 1.96 TeV. The data were collected with the D0 experiment at the Fermilab Tevatron Collider and correspond to an integrated luminosity of approximately 1 fb^-1. We search for e* in the process ppbar -> e* e, with the e* subsequently decaying to an electron plus photon. No excess above the standard model background is observed. Interpreting our data in the context of a model that describes e* production by four-fermion contact interactions and e* decay via electroweak processes, we set 95% C.L. upper limits on the production cross section ranging from 8.9 fb to 27 fb, depending on the mass of the excited electron. Choosing the scale for contact interactions to be Lambda = 1 TeV, excited electron masses below 756 GeV are excluded at the 95% C.L.