The stochastic method Kaos is an ad hoc construction in the line of metaheuristics designed to cope with the problem of structured motif discovery in a set of DNA sequences. Our contributions are: (1) the statement of a problem exceptionally formalized in the framework of operational research; (2) the design of an approach whose genuine novelty rests on driving the search by the (unknown) structure of the motif; (3) an analysis for establishing the soundness of the method including an original graphical evaluation of the risks to uncover false positive solutions; (4) the implementation of an accurate and robust tool well adapted to data mining (only 3 input parameters required). Therefore we contribute to bring knowledge about the accuracy and robustness of stochastic methods w.r.t. the hard and peculiar problem of biological sequence comparison.