The chemisorption of CHx (x = 0-3) fragments on a Pd(111) surface has been studied with density functional periodic calculations. The binding energy decreases strongly as the number of PI atoms increases, and the fragment tends to restore its tetravalency on the surface : carbon prefers a hollow site, the CH fragment is also in a hollow site, the CH2 is preferentially in a bridge, and the CH3 is on top of a Pd atom. On the surface the C-H bond cleavages are weakly endothermic, and the most stable surface species is CH3. Dehydrogenation to carbon is however possible through bimolecular reactions with simultaneous formation of CH4.