The method of integrating factors for the construction of conservation laws of a Chaplygin nonholonomic system is presented and studied. Based on the Chaplygin equations with canonical form, the integrating factors of the equations is defined, the necessary condition for the existence of conserved quantities of the system is given, and the conservation theorem and its inverse for the Chaplygin nonholonomic system are established. The studies show that for each group of nonsingular functions that correspond to the necessary condition, the system has a conserved quantity, while for a known conserved quantity, the corresponding integrating factor can be found, and the solution is not unique. Finally, we take an uniform sphere rolling on a perfectly rough horizontal plane as an example to discuss the application of the method.