An important problem in data and knowledge representation is the possibility of default rules that conflict. If the application of both of two default rules leads to a contradiction, they cannot both be applied. Systems that support the use of default rules may either remain indifferent or prioritize one rule over the other. In this paper a prioritized version of autoepistemic logic is presented. Priorities determine a subset of all stable expansions of a set, the preferred stable expansions. The priority notion is declarative, unlike e.g. some recent approaches to priorities in default logic that modify the semi-constructive definition of extensions of Reiter. Computationally the new priority notion can nevertheless be seen as a mechanism for pruning search trees in procedures for autoepistemic reasoning, as demonstrated by procedures given in the paper.