We analyze the chemical composition of the central star of the planetary nebula NGC 6543 based on a detailed NLTE model of its stellar wind. The logarithmic abundances by number are H = 12.00, He = 11.00, C = 9.03, N = 8.36, O = 9.02, Si = 8.19, P = 5.53, S = 7.57, and Fe = 7.24. Compared with the solar abundances, most of the elements have solar composition with respect to hydrogen, except C, which is overabundant by 0.28 dex, and Fe, which is depleted by ~0.2 dex. Contrary to most previous work, we find that the star is not H-poor and has a normal He composition. These abundances are compared with those found in the diffuse X-ray plasma and the nebular gas. Compared to the plasma emitting in diffuse X-rays, the stellar wind is much less depleted in iron. Since the iron depletions in the nebular gas and X-ray plasma are similar, we conclude that the plasma emitting diffuse X-rays is derived from the nebular gas rather than the stellar wind. Excellent agreement is obtained between the abundances in the stellar wind and the nebular recombination line abundances for He, C, and O relative to H. On the other hand, the derived stellar N abundance is smaller than the nebular N abundance derived from recombination lines and agrees with the abundance found from collisionally excited lines. The mean temperature variation determined by five different methods indicates that the difference in the nebular abundances between the recombination lines and collisionally excited lines can be explained as due to the temperature variations in a chemically homogeneous medium.