The high peak-to-average-power ratio (PAPR) of orthogonal frequency-division multiplexing (OFDM) degrades the performance in optical wireless communication systems. This paper proposes a modified asymmetrically clipped optical OFDM (ACOOFDM) with low PAPR via introducing a recoverable upper-clipping (RoC) procedure. Although some information is clipped by a predetermined peak threshold, the clipped error information is kept and repositioned in our proposed scheme, which is named RoC-ACO-OFDM, instead of simply being dropped in conventional schemes. The proposed method makes full use of the specific structure of ACO-OFDM signals in the time domain, where half of the positions are forced to zeros within an OFDM symbol. The zero-valued positions are utilized to carry the clipped error information. Moreover, we accordingly present an optimal maximum a posteriori (MAP) detection for the RoC-ACO-OFDM system. To facilitate the usage of RoC-ACO-OFDM in practical applications, an efficient detection method is further developed with near-optimal performance. Simulation results show that the proposed RoC-ACO-OFDM achieves a significant PAPR reduction, while maintaining a competitive bit-error rate performance compared with the conventional schemes.