In this paper, a downlink multi-carrier cognitive radio (CR) network is considered. The CR network consists of one cognitive base station (CBS) and a set of secondary users (SUs) sharing the same spectrum with the primary user (PU). Chunk-based resource allocation is adopted where subcarriers are grouped into chunks for allocation to the SUs. The problem of chunk-based resource allocation under the interference power constraint and the transmit power constraint is investigated. The objective is to maximize the sum rate of the SUs. For this, based on Lagrange dual method, a near-optimal joint chunk and power allocation scheme is proposed. The complexity of the optimal scheme is exponential in the number of chunks, while the complexity of the proposed scheme is reduced significantly to only linear in the number of chunks, and at the same time, it is shown that the proposed scheme achieves almost the same performance that can be achieved by the optimal scheme. The impacts of the interference power constraint, the transmit power constraint, number of subcarriers within the chunk and the channel coherence bandwidth on the performance of the proposed scheme are investigated. Particularly, it is shown that increasing the channel coherence bandwidth does not always lead to improvement of the SU performance.