The fractional Fourier transform (FRFT), which is a family of linear transformations generalizing the classical Fourier transform, has been used in the fields of filter design, signal processing, phase retrieval, and pattern recognition due to its unique properties. The FRFT of a signal can be interpreted as a decomposition of the signal in terms of chirps. In this paper, for the first time, to the best of our knowledge, we introduce an optical FRFT (OFRFT)based orthogonal frequency division multiplexing (OFDM) visible light communications (VLC) system and compare numerical results with a direct current-biased optical (DCO)-OFDM system. First, the optimal fractional order is calculated to improve the performance of the proposed system by minimizing the bit error rate (BER). The numerical results show that OFRFT-OFDM with the optimal fractional order offers a significantly improved BER performance compared with DCO-OFDM under the same computational complexity and spectral efficiency. In addition, the peak to average power ratio, which is an issue in light emitting diode-based VLC systems, is reduced by <1 dB using OFRFT-OFDM for the same BER compared with DCO-OFDM.