The capacity of the intensity-modulation directdetection optical broadcast channel (OBC) is investigated, under both average and peak intensity constraints. An outer bound on the capacity region is derived by adapting Bergmans’ approach to the OBC. Inner bounds are derived by using superposition coding with either truncated-Gaussian (TG) distributions or discrete distributions. While the discrete distribution achieves higher rates, the TG distribution leads to a simpler representation of the achievable rate region. At high signal-to-noise ratio (SNR), it is shown that the TG distribution is nearly optimal. It achieves the symmetric-capacity within a constant gap (independent of SNR), which approaches half a bit as the number of users grows. It also achieves the capacity region within a constant gap. At low SNR, it is shown that on-off keying (OOK) with time-division multipleaccess (TDMA) is optimal. This is interesting in practice since both OOK and TDMA have low complexity. At moderate SNR (typically [0,8] dB), a discrete distribution with a small alphabet size achieves fairly good performance.