Surveying genome-wide coding variation within and among species gives unprecedented power to study the genetics of adaptation, in particular the proportion of amino acid substitutions fixed by positive selection. Additionally, contrasting the autosomes and the X chromosome holds information on the dominance of beneficial (adaptive) and deleterious mutations. Here we capture and sequence the complete exomes of 12 chimpanzees and present the largest set of protein-coding polymorphism to date. We report extensive adaptive evolution specifically targeting the X chromosome of chimpanzees with as much as 30% of all amino acid replacements being adaptive. Adaptive evolution is barely detectable on the autosomes except for a few striking cases of recent selective sweeps associated with immunity gene clusters. We also find much stronger purifying selection than observed in humans, and in contrast to humans, we find that purifying selection is stronger on the X chromosome than on the autosomes in chimpanzees. We therefore conclude that most adaptive mutations are recessive. We also document dramatically reduced synonymous diversity in the chimpanzee X chromosome relative to autosomes and stronger purifying selection than for the human X chromosome. If similar processes were operating in the human-chimpanzee ancestor as in central chimpanzees today, our results therefore provide an explanation for the much-discussed reduction in the human-chimpanzee divergence at the X chromosome.