Results of a study of the substructure of the highest transverse momentum (pT) jets observed by the CDF collaboration are presented. Events containing at least one jet with pT > 400 GeV/c in a sample corresponding to an integrated luminosity of 5.95 inverse fb, collected in 1.96 TeV proton-antiproton collisions at the Fermilab Tevatron collider, are selected. A study of the jet mass, angularity, and planar-flow distributions is presented, and the measurements are compared with predictions of perturbative quantum chromodynamics. A search for boosted top-quark production is also described, leading to a 95% confidence level upper limit of 38 fb on the production cross section of top quarks with pT > 400 GeV/c.