It would only appear in one race, the 1968 French Grand Prix at Rouen-Les-Essarts, driven by Jo Schlesser. Schlesser was chosen to drive the RA302 because normal Honda driver John Surtees (who was the 1964 world champion) refused to drive it as he deemed it to be unsafe and labelled it as a "potential deathtrap". This was proven on lap two of the Grand Prix; Schlesser crashed at the Virage des Six Frères section of the circuit and the car came to rest sideways against a bank. The magnesium-bodied Honda and 58 laps worth of fuel ignited instantly, killing Schlesser and destroying the original RA302.
A second RA302 was built, with slight modifications, earmarked for Surtees to drive at the next race, but when Surtees again refused to drive it, Honda decided to pull out of Grand Prix racing and did not return as a constructor until the 2006 Formula One season with the Honda RA106. The RA302 intended for Surtees at the Italian Grand Prix is now shown at the Honda Collection Hall.