We report on a measurement of the mass dependence of the
forward-backward charge asymmetry, A_FB, and production cross section d
sigma/dM for e+ e- pairs with mass M_ee > 40 GeV/c2. The data sample
consists of 108 pb-1 of p anti-p collisions at s**(1/2) = 1.8 TeV taken by the
Collider Detector at Fermilab during 1992-1995. The measured asymmetry and
d sigma/dM are compared with the predictions of the Standard Model and a
model with an extra Z' gauge boson.