Chemisorbed hydrogen and various intermediate hydrocarbon fragments play an important role in the important reaction of ethylene hydrogenation to ethane, which is catalyzed by Pt(lll). As a first step toward building a theoretical mechanism of the ethylene hydrogenation process, binding site preferences and geometries of chemisorbed hydrogen, methyl, and ethyl on the Pt(lll) surface are presented and rationalized. State-of-the-art Pseudopotential Planewave Density Functional Theory is employed for calculating accurate binding energies and geometries for the adsorbates. A comprehensive theory of hydrogen and methyl chemisorption on Pt(lll) is developed with the help of Crystal Orbital Hamilton Population formalism within the extended Huckel molecular orbital theory. The symmetry properties of the surface Pt orbitals as well as the mixing of Pt s, p, and d orbitals in pure Pt is shown to be crucial in determining the strength of subsequent interaction with an adsorbate. It is suggested that hydrogen moves freely on the Pt(lll) surface while the methyl and ethyl groups are essentially pinned on the atop position. Strong agostic interactions between C-H bonds and surface Pt are proposed for methyl and ethyl on higher symmetry sites. The different nature of chemisorption on Pt and Ni surfaces is speculated. Theoretical results presented in this paper are generally consistent with the available experimental data.