A fundamental step in the replication of a viral particle is the self-assembly of its rigid shell (capsid) from its constituent proteins. Capsids play a vital role in genome replication and intercellular movement of viruses, and as such, understanding viral assembly has great potential in the development of new antiviral therapies and a systematic treatment of viral infection. In this article, we assume that nucleation is the underlying mechanism for self-assembly and combine the theoretical methods of the physics of equilibrium polymerization with those of the classical nucleation to develop a theory for the kinetics of virus self-assembly. We find expressions for the size of the critical capsid, the lag time, and the steady-state nucleation rate of capsids, and how they depend on both protein concentration and binding energy. The latter is a function of the acidity of the solution, the ionic strength, and the temperature, explaining why capsid nucleation is a sensitive function of the ambient conditions.