This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundesministerium für Bildung und Forschung, Germany; the Korean World Class University Program, the National Research Foundation of Korea; the Science and Technology Facilities Council and the Royal Society, United Kingdom; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovación, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; the Academy of Finland; the Australian Research Council (ARC); and the EU community Marie Curie Fellowship Contract No. 302103. This work was also supported by the Shrum Foundation, the Weizman Institute of Science and the Israel Science Foundation. 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 fb−1, 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. Peer Reviewed et al.