We have measured the cross section as a function of invariant mass for isolated electron pairs produced in p anti-p collisions at s**(1/2) = 1.8 TeV for pair masses M > 30 GeV/(c**2). We find good agreement between the measured distribution and the Standard Model prediction for the Drell-Yau production mechanism. Additional heavy neutral vector bosons (Z') are excluded for M(Z') < 387 GeV/c**2) (95% confidence level) assuming Standard Model couplings. A lower limit of 2.2 TeV (95% confidence level) is placed on the electron-quark compositeness scale parameter Lambda(L anti-L) associated with an effective contact interaction.