We consider the possibility of using a gauge singlet scalar as the source of the additional CP violation needed to allow the observed baryon (B) number asymmetry to be generated during the electroweak phase transition. In addition to extending the standard SU(3) X SU (2) X U(1) model by a gauge singlet scalar, it is also necessary to add additional fields, in order to transmit CP violation from the singlet scalar sector to the quarks and so to the B number violating processes in the early Universe. We consider the case of a second Higgs doublet, with Yukawa couplings to the quarks and leptons which are proportional to those of the standard model Higgs in order to avoid large FCNC effects. For reasonable values of the couplings of the gauge singlet scalar it is possible to generate the observed B asymmetry. A specific example is discussed for which we show that the singlet scalar expectation value goes to zero for temperatures below the electroweak phase transition temperature, allowing the model to avoid strong CP violation effects due to spontaneous CP violation and domain wall problems due to discrete symmetry breaking. In this case the singlet scalars are cosmologically stable and can naturally account for the cold dark matter in the Universe. Possible resolutions of the Higgs mass problem of electroweak baryogenesis within the framework of the model are also discussed.