Many wireless systems exploit transmit diversity for more reliable detection of signals at the receiver. To accomplish this, coding is spread across multiple transmit antennas. An example of this is the well known "Alamouti transmit diversity", where a very simple coding scheme across multiple transmit antennas allows systems to attain performance similar to systems with multiple receive antennas. The major drawback is that this system only works when a "flat-fading" model for the channel is assumed; when used in a multipath environment, the system breaks down. Here we show that when the Alamouti code is placed within an OFDM structure, using adjacent frequency bands rather than consecutive symbol intervals, it can asymptotically achieve the same performance in multipath fading as the Alamouti code in flat-fading.