In this paper, a method called Offset Modulation (OM-OFDM) is proposed to control the Peak-to Average Power Ratio (PAPR) of an Orthogonal Frequency Division Multiplexing (OFDM) signal. The theoretical bandwidth occupancy of the proposed offset modulated signal is derived. Using these bandwidth occupancy results, a closed-form theoretical Bit Error Rate (BER) expression for an offset modulated transmission is derived and validated. Thereafter, a BER comparison between OM-OFDM and OFDM at a PAPR value of 13 dB shows that both methods offer similar BER characteristics for frequency selective fading channel conditions. The OM-OFDM method in addition is able to accurately control the PAPR of a transmission for a targeted BER.