We have developed a prototype multi-gap Resistive Plate Chamber (RPC) for a time-of-flight (TOF) detector at the J-PARC π20 beam line. It is a double stack RPC with five 0.26-mm gas gaps in each stack. Its readout strips are 25 mm wide and 940 mm long. We have also developed an amplifier board which can be used for TOF-RPCs in general and carried out a beam test to evaluate the performance of the RPC and this new board. Timing measurements and a time-walk correction using a time-over-threshold (TOT) method were found to work well without stretching signals. We obtained time resolutions of 60-70 ps when the test particle’s position was determined using 5 mm × 10 mm trigger detectors and 65-80 ps without this position determination.