The dilepton mass spectrum in ppbar -> l^+l^- + X interactions is
studied using dielectrons (ee) and dimuons (mu mu) in 110 pb^-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 g^2_0/4 pi = 1, limits on chiral quark-electron and quark-muon
compositeness scales in the range of 2.5 to 4.2eV are obtained.