The kinetic energy dependence of the reaction of Zr+(F-4) with methane has been studied using guided ion beam mass spectrometry. At low energies, the only process observed is dehydrogenation, which is slightly endothermic such that it exhibits a strong isotope effect when CD4 is used as the reactant. At high energies, products resulting from C-H cleavage processes are appreciable. Modeling of the endothermic reaction cross sections yields the 0 K bond dissociation energies (in eV) of D-0(Zr+-CH) = 5.96 +/- 0.22, D-0(Zr+-CH2) = 4.62 +/- 0.07, and D-0(Zr+-CH3) = 2.30 +/- 0.24. The experimental thermochemistry is favorably compared with density functional theory calculations (B3LYP), which also establish the electronic structures of these species and provide insight into the reaction mechanism. The results for Zr+ are compared with those for the first-row transition metal congener Ti+, and the differences in behavior and mechanism are discussed.