This letter presents a novel opportunistic cooperative positioning approach for orthogonal frequency-division multiple access (OFDMA) systems. The basic idea is to allow idle mobile terminals (MTs) opportunistically estimating the arrival timing of the training sequences for uplink synchronization from active MTs. The major advantage of the proposed approach over state-of-the-arts is that the positioning-related measurements among MTs are performed without the paid of training overhead. Moreover, Cramer-Rao lower bound (CRLB) is utilized to derive the positioning accuracy limit of the proposed approach, and the numerical results show that the proposed approach can improve the accuracy of non-cooperative approaches with the a-priori stochastic knowledge of clock bias among idle MTs.