Catalytic groundwater remediation from chlorinated organic solvents like trichloroethene (TCE) has been found to be more effective and sustainable than traditional non-destructive methods. Among the experimentally studied catalyst materials, Pd-decorated Au nanoparticles show the highest activity and selectivity combined with the best resistance towards poisoning by chemicals present in groundwater. In this study the thermochemistry and adsorption geometries of TCE and its hydrodechlorination products are investigated via density functional theory calculations. Various model systems for Pd-supported Au nanoparticles are addressed. The adsorption of TCE is endothermic on bare Au(111), almost thermoneutral or slightly exothermic on Pd-Au surface alloys and clearly exothermic on Pd overlayer structures on Au(111). The strongest chemisorption is on the di-σ configuration between Pd atoms over the smallest 2D Pd clusters containing only a few Pd atoms. These are not, however, the best catalysts as they are too small to co-adsorb hydrogen needed for hydrodechlorination reaction. We demonstrate good correlation between adsorption energies and the d-band center of the system. The variation of adsorption energy from the one Pd-Au composition to the other can be tentatively assigned to be due to the ligand and coordination effects. Also, the ensemble effects are important; without the right ensemble the adsorption is weak or endothermic.