Unless you choose a line of diapers specifically created to be chemical-free, assume your diapers will contain chemicals, the five most common being polyethylene, polypropylene, chlorine, dyes, and fragrances (source).
All perform a specific function. For example, both polyethylene and polypropylene are plastics to improve absorbency and waterproof the diaper. Chlorine bleaches the inner lining and fragrances help mask nasty smells.
While your baby may have a sensitivity to some of these and have a bad reaction, the chemicals used in disposable diapers are either non-toxic and safe for your baby to wear, or in such low quantities that harmful reactions are highly unlikely (source).