Highly luminous rapid flares are characteristic of processes around compact objects like white dwarfs, neutron stars and black holes. In the high-energy regime of X-rays and gamma-rays, outbursts with variabilities on timescales of seconds or less are routinely observed, for example in gamma-ray bursts or soft gamma-ray repeaters. At optical wavelengths, flaring activity on such timescales has not been observed, other than from the prompt phase of one exceptional gamma-ray burst. This is mostly due to the fact that outbursts with strong, fast flaring are usually discovered in the high-energy regime; most optical follow-up observations of such transients use instruments with integration times exceeding tens of seconds, which are therefore unable to resolve fast variability. Here we show the observation of extremely bright and rapid optical flaring in the Galactic transient SWIFT J195509.6+261406. Our optical light curves are phenomenologically similar to high-energy light curves of soft gamma-ray repeaters and anomalous X-ray pulsars, which are thought to be neutron stars with extremely high magnetic fields (magnetars). This suggests that similar processes are in operation, but with strong emission in the optical, unlike in the case of other known magnetars.