For a single carrier frequency division multiple access (SC-FDMA) system, we obtain the jointly optimal power and chunk allocation policies which maximize the sum rate. Our solution is applicable to both localized and interleaved subcarrier mapping schemes. We solve the joint optimization problem by sequentially solving two sub-problems: power allocation and chunk allocation. Primarily, we use an optimal power allocation algorithm, which we derive from Karush-Kuhn-Tucker (KKT) conditions; and then we convert the optimum chunk assignment problem into a maximum weighted matching problem on a bipartite graph, and hence solve it in polynomial time. We also propose two greedy chunk allocation algorithms with lower complexity, and demonstrate that these algorithms produce near optimal results, especially for interleaved subcarrier mapping, when used in conjunction with optimal power control.