A kinetic theory describing chemical reactions on crystal surfaces is introduced. Kinetic equations are used to model physisorbed-gas particles and chemisorbed particles interacting with fixed potentials and colliding with phonons. The phonons are assumed to be at equilibrium and the physisorbed-gas and chemisorbed species equations are coupled to similar kinetic equations describing crystal atoms on the surface. An arbitrary number of surface species and heterogeneous chemical reactions are considered, covering Langmuir-Hinshelwood as well as Eley-Rideal mechanisms and the species may be polyatomic. A kinetic entropy is introduced for the coupled system and the H theorem is established. Using a fluid scaling and a Chapman-Enskog method, fluid boundary conditions are derived from the kinetic model and involve complex surface chemistry as well as surface tangential multicomponent diffusion.