Coherent Optical OFDM (CO-OFDM) has been demonstrated for delivering superior performance in spectral efficiency, receiver sensitivity, and polarization-dispersion resilience. Fueled by the rapid advancement in semiconductor technology, high-speed field-programmable gate arrays (FPGA) and analogue-to-digital-converters/digital-to-analogue converters (ADC/DACs) have been increasingly adopted for digital signal processing in optical communications. In this paper, we report the first FPGA-based real-time implementation of coherent optical OFDM (CO-OFDM) receiver with a transmission rate up to 3.1 Gb/s. Several basic aspects of CO-OFDM signal processing are described in detail, and the BER sensitivity performance are evaluated in real-time. To the best of our knowledge, we have achieved the record real-time reception date rate for a single-input single-output (SISO) coherent OFDM signal, in either RF domain or optical domain.