In this paper, we investigate the information theoretical performance of a cooperative OFDM (orthogonal frequency division multiplexing) system with imperfect channel estimation. Assuming the deployment of a training-aided channel estimator, we derive a lower bound on the achievable rate for the cooperative OFDM system with amplify-and-forward relaying over frequency-selective Rayleigh fading channels. The bound is later utilized to optimally allocate power between the training and data transmission phases for the cooperating nodes. Monte-Carlo simulations demonstrate that the proposed power allocation scheme brings 5 to 15 percent improvement in the achievable rate.