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Chaotic sequences may be advantageous for secure communications. Although many chaotic communications systems have been proposed, most of them show a poor performance under realistic channel conditions (i.e. noise and multipath fading). In this paper, we propose a novel chaotic modulation scheme based on the symbolic sequence associated to the chaotic map and backward iteration. These chaotically modulated signals are then sent in each sub-carrier of a conventional OFDM system instead of the usual BPSK or QAM ones. In the receiver, equalization is performed in the frequency domain, and the Viterbi algorithm is used to estimate the transmitted sequence. Computer simulations confirm the good performance of the proposed approach.