An analysis of the CP violating asymmetry in K + /-->(3π) + /- decays in the Standard Model and, by means of the mass insertion approximation, in a wide class of possible supersymmetric extensions, is presented. We find that the natural order of magnitude for this asymmetry is O(10 - 5 ) in both cases. Within supersymmetric models effects as large as O(10 - 4 ) are possible, but only in a restricted range of the relevant parameters.