  In this article we prove an analogue of the equidistribution of preimages
theorem from complex dynamics for maps of good reduction over nonarchimedean
fields. While in general our result is only a partial analogue of the complex
equidistribution theorem, for most maps of good reduction it is a complete
analogue. In the particular case when the nonarchimedean field in question is
equipped with the trivial absolute value, we are able to supply a strengthening
of the theorem, namely that the preimages of any tame valuation equidistribute
to a canonical measure.
