The problem of Blind source extraction(BSE) regarding a chaotic signal is addressed in this paper, by employing the newly defined Proliferation exponent(PE). The properties of gradient pursuit algorithm based on PE are further articulated, especially the infelicity to tackle a BSE problem. Subsequently, we devise a constraint optimization algorithm called Orthogonal random searching(ORS) to accomplish the optimization task,which in essence searches for optimal solutions with the principle of Markov chain Monte Carlo(MCMC). Experimental results reveal that this PE-based random searching method can extract the desired chaotic signal among multiple Gaussian mixtures, as well as showing robustness against noise contamination. The problem of Blind source extraction (BSE) regarding a chaotic signal is addressed in this paper, by employing the newly defined Proliferation exponent (PE). The properties of gradient pursuit algorithm based on PE are further articulated, especially the infelicity to tackle a BSE problem., we devise a constraint optimization algorithm called Orthogonal random searching (ORS) to achieve the optimization task with the principle of Markov chain Monte Carlo (MCMC). Experimental results reveal that this PE-based random searching method can extract the desired chaotic signal among multiple Gaussian mixtures, as well as showing robustness against noise contamination.