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Orthogonal frequency-division multiplexing (OFDM) has been widely studied and adopted in visible-light communication (VLC) systems because of its high spectral efficiency and low-complexity implementation. However, OFDM-based VLC systems suffer from a high peak-to-average power ratio (PAPR), along with the nonlinear transfer characteristics of light-emitting diodes (LEDs). In this paper, a subcarrier grouping scheme for an OFDM-based VLC system is proposed. This scheme exploits the property that one LED lamp usually contains multiple independent LED chips. In the proposed scheme, all OFDM signal subcarriers are divided into groups, and each group is transmitted by an individual LED chip while the same receiver structure is maintained. The PAPR is reduced significantly because only some of the subcarriers are located on each LED chip. Hence, the achievable input power can be increased, leading to a higher signal-to-noise ratio (SNR) and a lower bit error rate (BER). Simulated and experimental results demonstrate that the BER performance can be improved by over two orders of magnitude. Moreover, an adaptive switching mechanism is also proposed in this paper, in which a subcarrier grouping scheme is employed adaptively when the required input power is high. Simulation results validate that the proposed mechanism can enhance system robustness significantly.