We extend the idea of end-to-end learning of communications systems through deep neural network (NN)-based autoencoders to orthogonal frequency division multiplexing (OFDM) with cyclic prefix (CP). Our implementation has the same benefits as a conventional OFDM system, namely singletap equalization and robustness against sampling synchronization errors, which turned out to be one of the major challenges in previous single-carrier implementations. This enables reliable communication over multipath channels and makes the communication scheme suitable for commodity hardware with imprecise oscillators. We show that the proposed scheme can be realized with state-of-the-art deep learning software libraries as transmitter and receiver solely consist of differentiable layers required for gradient-based training. We compare the performance of the autoencoder-based system against that of a state-of-the-art OFDM baseline over frequency-selective fading channels. Finally, the impact of a non-linear amplifier is investigated and we show that the autoencoder inherently learns how to deal with such hardware impairments.