We propose a transmit diversity scheme for frequency selective fading channels using orthogonal frequency division multiplexing (OFDM). The transmit diversity scheme proposed by Alamouti (see IEEE JSAC, vol.16, no.8, p.1451-58, 1998) for flat fading channels is extended to the case when the channel has a delay spread. There is no loss in receive SNR due to the delay spread in the channel. A diversity order of 2N can be achieved by using two transmit and N receive antennas. We discuss several interesting aspects of the approach and compare it with other extensions of the Alamouti scheme for delay spread channels.