Charge trapping by intrinsic surface states on β-Si3N4 surfaces is a relatively unexplored topic in the study of the electronic properties of this material. In the present work, ab-initio density functional theory is used to observe the transfer of an electron from a substitutional-oxygen donor impurity to a coordinatively-unsaturated surface site on the (0001) surface. The process occurs spontaneously, with little or no activation energy, and has a profound effect on surface electronic structure that leads to a range of different states distributed throughout the band gap. The results are discussed in relation to experimentally-observed surface charging that depends on O2 exposure. The related issue of the β-Si3N4 band gap, which has been somewhat controversial, is also discussed in light of recent experimental and theoretical results.