We present a measurement of the inclusive jet cross section in p anti-p
collisions at s**(1/2) = 1.8 TeV at the Fermilab Tevatron using the Collider
Detector at Fermilab (CDF).  Good agreement is seen with the predictions of
recent next-to-leading (O(alpha**3(s))) predictions.  The dependence of the
cross section on clustering size is measured.  An improved limit on Lambda(c),
a term characterizing possible quark substructure, is set at 1.4 TeV (95& CL).