Activation of methane by the third-row transition-metal cation Os+ is studied experimentally by examining the kinetic energy dependence of reactions of Os+ with CH4 and CD4 using guided-ion-beam tandem mass spectrometry. A flow tube ion source produces Os+ in its electronic ground state and primarily in the ground spin-orbit level. Dehydrogenation to form [Os,C,2H](+)+H-2 is exothermic, efficient, and the only process observed at low energies for reaction of Os+ with methane, whereas OsH+ dominates the product spectrum at higher energies. The kinetic energy dependences of the cross sections for several endothermic reactions are analyzed to give 0K bond dissociation energies (in eV) of D-0(Os+C)=6.20 +/- 0.21, D-0(Os+CH)=6.77 +/- 0.15, and D-0(Os+CH3)=3.00 +/- 0.17. Because it is formed exothermically, D-0(Os+CH2) must be greater than 4.71eV, and a speculative interpretation suggests the exothermicity exceeds 0.6eV. Quantum chemical calculations at the B3LYP/def2-TZVPP level show reasonable agreement with the experimental bond energies and with previous theoretical values available. Theory also provides the electronic structures of the product species as well as intermediates and transition states along the reactive potential energy surfaces. Notably, the structure of the dehydrogenation product is predicted to be HOsCH+, rather than OsCH2+, in contrast to previous work.