In the limit of the strong magnetic field , the closed hierarchy of kinetic equations for correlation functions of an arbitrary order is derived for a one-dimensional kinetic Ising model. This hierarchy allows asymptotically exact solution in quadratures. For the first time the closed set of equation for generating functions of the domain distribution of the identically oriented spins have been obtained. The relations between kinetic parameters that make it possible to find exact solutions in quadratures are indicated.