This paper deals with the resource allocation task for the uplink of OFDMA-based cognitive radio (CR) systems. A weighted sum-rate maximization problem is formulated to optimize the subcarrier assignment as well as the power loading per CR user, while protecting the primary user (PU) systems. Since the CR-to-PU channels may not be accurately acquired, the PU interference constraint is cast as a chance constraint. Consequently, a convex conservative approximation of the chance constraint is employed for tractability reasons. In particular, to mitigate the combinatorial complexity incurred for optimal subcarrier assignment, a separable structure is pursued, and the dual decomposition method is employed to obtain a near-optimal solver. The resultant algorithm is tested via simulated tests.