Visible light communications (VLC), a short-range optical wireless communication scheme using light-emitting diodes (LEDs) as transmitters, has been proposed to support multiple users, predominantly in indoor environments. This paper explores using orthogonal frequency division multiple access (OFDMA) for VLC due to its high spectrum utilization efficiency and potentially high transmission data rate. The proposed optical OFDMA uses adjacent subcarriers as a set to support each user. Doing so allows some users to sample at a lower sampling rate and employ a smaller fast Fourier transform (FFT) to lower the computational complexity and hardware cost. A multi-cell structure is naturally obtained in VLC since more than one LED lamp is usually installed in an indoor environment. In this paper, users located in different cells can reuse the same subcarrier sets, potentially causing multiple access interference. Analysis and simulation results are used to predict the subcarrier-set reuse probability over the entire indoor space. When the OFDM modulation index is optimized considering the peak-power-limit of the LEDs, the average transmission data rate is twice that of using OFDM that does not reuse the spectral resources, for the scenarios tested.