The dilepton mass spectrum in p¯p→l+l−+X interactions is studied using dielectrons (ee) and dimuons (μμ) in 110pb−1 of data collected with the Collider Detector at Fermilab. The data are consistent with standard model predictions. The mass spectrum, being a probe for new physics, is examined for new interactions of quarks and leptons from a common composite structure. Assuming a contact interaction with the conventional coupling g20/4π=1, limits on chiral quark-electron and quark-muon compositeness scales in the range of 2.5 to 4.2 TeV are obtained.