In this paper, a novel paradigm of constructing measurement matrices is proposed for compressive sensing. More precisely, the chaotic bipolar sequences ({1,− 1} elements) are utilized to build binarization measurement matrices of general size. By means of concentration inequalities together with covering argument, we show that our proposed bipolar matrices meet the restricted isometry property, which can ensure exact recovery from the linear samples. Moreover, numerical experiments illustrate that the proposed matrices outperform its counterparts, such as random Gaussian matrix. For practical applications, our proposed matrices are highly efficient for storage, multiplier and rapid data acquisition, and hardware realization. We hope that our framework reveals new directions for practitioners, as it attempts to put some of the chaos theory in perspective for practical compressive sensing applications.