We address the issue of structured motif inference. This problem is stated as follows: given a set of n DNA sequences and a quorum q (%), find the optimal structured consensus motif described as gaps alternating with specific regions and shared by at least q x n sequences. Our proposal is in the domain of metaheuristics: it runs solutions to convergence through a cooperation between a sampling strategy of the search space and a quick detection of local similarities in small sequence samples. The contributions of this paper are: (1) the design of a stochastic method whose genuine novelty rests on driving the search with a threshold frequency f discrimining between specific regions and gaps; (2) the original way for justifying the operations especially designed; (3) the implementation of a mining tool well adapted to biologists' exigencies: few input parameters are required (quorum q, minimal threshold frequency f, maximal gap length g). Our approach proves efficient on simulated data, promoter sites in Dicot plants and transcription factor binding sites in E. coli genome. Our algorithm, Kaos, compares favorably with MEME and STARS in terms of accuracy.