Analysis of the spatial dependence of current-voltage characteristics obtained from scanning tunneling microscopy experiments indicates that the charge density wave (CDW) occurring in NbSe_{2} is subject to locally strong pinning by a non-negligible density of defects, but that on the length scales accessible in this experiment the material is in a "Bragg glass" phase where dislocations and antidislocations occur in bound pairs and free dislocations are not observed. An analysis based on a Landau theory is presented showing how a strong local modulation may produce only a weak long range effect on the CDW phase.