A PE-ACO-OFDM (Position-Encoded Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing) signaling scheme for intensity modulation and direct detection is introduced in this paper, where the anti-asymmetry characteristics of ACO-OFDM are exploited to improve the rate of data transmission. This is achieved by reducing the symbol duration of the ACO-OFDM signal, where only the first half of ACO-OFDM is used to transmit the ACO-OFDM data symbol after inverting its negative samples to positive ones. In addition, encoded ACO-OFDM samples are combined with every ACO-OFDM symbol to allow the receiver to identify the position of the inverted samples. Simulation results are introduced, and it is shown that the data rates of PE-ACO-OFDM improve by 33% compared with ACO-OFDM, when a 256-quadrature amplitude modulation scheme is considered as the encoded constellation order. It is also shown that the signal to noise ratio of the proposed PE-ACO-OFDM is higher by almost 1 dB compared with the traditional ACO-OFDM.