[en] We consider a deformed superspace in which the coordinates θ do not anticommute, but satisfy a Clifford algebra. We present results on the properties of N = 1/2 supersymmetric theories of chiral superfields in deformed superspace, taking the Wess-Zumino model as the prototype. We prove new (non)renormalization theorems: the F-bar -term is radiatively corrected and becomes indistinguishable from the D-term, while the -term is not renormalized. Supersymmetric vacua are critical points of the antiholomorphic superpotential. The vacuum energy is zero to all orders in perturbation theory. We illustrate these results with several examples. (author)