Slicing is a program analysis technique originally developed by Weiser for imperative languages. Weiser showed that slicing is a natural tool for debugging, but it has other numerous applications (program integration, program optimization, etc.) In this article we describe a backward slicing algorithm for Prolog which produces executable slices. The proposed algorithm is applicable at least to pure Prolog extended by some simple built-in predicates that handle the explicit unification =/2 and arithmetic. To our knowledge, this algorithm is the first one to be proposed for Prolog. Because of the indeterminism and lack of explicit control flow of Prolog, existing algorithms cannot be trivially adapted. The two main contributions of this paper are a general definition of slicing adapted to Prolog and a slicing algorithm that produces executable programs.