In this paper we derive information theoretic results for asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) in an intensity modulated direct detection (IM/DD) optical communication system subject to a range of constraints. ACO-OFDM is a form of OFDM designed for IM/DD systems. It is an effective solution to intersymbol interference (ISI) caused by a dispersive channel and also requires less optical power than conventional optical modulation formats. Although the classical Shannon capacity formula cannot be applied directly to an IM/DD system, we show that when ACO-OFDM is used in an IM/DD system, it can be adapted to calculate the information rate of the data-carrying odd frequency subcarriers. As a result conventional water filling techniques can be used for a frequency selective channel. These results are applied to indoor wireless systems using realistic parameters for the transmitter, receiver and channel. The maximum rate at which data can be transmitted depends on the channel, the electrical bandwidth and the transmitted optical power. Even when there is no line of sight (LOS) path, when the electrical bandwidth is limited to 50 MHz and the average optical power is limited to 0.4 W, data rates of approximately 80 Mbit/s can theoretically be achieved.