We make a Monte Carlo study on compositeness of first generation quarks and leptons using the Drell-Yan distribution in the high dielectron mass region at the Tevatron and LHC energies. The current experimental lower limits on the compositeness scale, Lambda, vary from 2.5 to 6.1 TeV. In the present analysis, we assume that there will be no deviation of the dielectron mass spectrum from Standard Model prediction at center of mass energy 2 TeV (Tevatron) and 14 TeV (LHC). We then find that in the LL, RR, RL and LR chirality channels of the quark-electron currents, it is possible to extend the lower limits on Lambda (at 95% {CL}) to a range of 6 to 10 TeV for 2 fb^{-1} and 9 to 19 TeV for 30 fb^{-1} of integrated luminosity at Tevatron. At LHC, the corresponding limits extend to a range of 16 to 25 TeV for 10 fb^{-1} and 20 to 36 TeV for 100 fb^{-1} of integrated luminosity.
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