The Cahn-Hilliard equation is of importance in materials science and a range of other fields. It represents a diffuse interface model for simulating the evolution of phase separation in solids and fluids, and is a nonlinear fourth-order parabolic equation, which makes its numerical solution particularly challenging. To this end, a finite element formulation has been developed which can solve the Cahn-Hilliard equation in its primal form using C^0 basis functions. Here, analysis of a fully discrete version of this method is presented in the form of a priori uniqueness, stability and error analysis.