  We consider a deformed superspace in which the coordinates \theta 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-term is radiatively corrected and becomes
indistinguishable from the D-term, while the Fbar-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.
