We address the difficult 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, Kaos, is in the domain of metaheuristics: it runs solutions to convergence through a cooperation between the generation of starting points in the search space and the refinement of the best candidate solutions. The contributions of this paper are: (i) 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; (ii) the proposal of a method for prooving the soundness of our stochastic process otherwise than formally (which is impossible) and otherwise than empirically (which is done anyway); (iii) the implementation of a tool well adapted to biological data mining: few input parameters are required (q, f and the maximal gap length g). Kaos proves efficient on simulated data, promoter sites in Dicot plants and transcription factor binding sites in E. coli genome. It compares favorably with MEME and STARS in terms of accuracy.