We have used 106 pb^-1 of data collected in ppbar collisions at
sqrt s = 1.8 TeV by the Collider Detector at Fermilab to measure jet angular
distributions in events with two jets in the final state.  The angular
distributions agree with next to leading order predictions of QCD in all dijet
invariant mass regions.  The data exclude at 95% CL a model of quark
substructure in which only up and down quarks are composite and the contact
interaction scale is Lambda^+_ud \leq 1.6 TeV or Lambda^-_ud \leq 1.4 TeV.
For a model in which all quarks are composite the excluded regions are
Lambda^+ \leq 1.8 TeV and \Lambda^- \leq 1.6 TeV.