  The extreme TeV blazar 1ES 0229+200 is a high-frequency-peaked BL Lacertae
object. It has not shown intraday variability in extensive optical and X-ray
observations. Nor has it shown any significant variability on any measurable
timescale in the 1-100 GeV energy range over a 14-year span, but variations in
the source flux around its average are present in the energy range above 200
GeV. We searched for intraday optical variability in 1ES 0229+200 as part of an
ongoing project to search for variability and quasi-periodic oscillations in
the high-cadence, nearly uniformly sampled optical light curves of blazars
provided by the Transiting Exoplanet Survey Satellite (TESS). 1ES 0229+200 was
monitored by TESS in its Sectors 42, 43 and 44. We analysed the data of all
these sectors both with the TESS provided lightkurve software and the eleanor
reduction pipeline. We detected a strong, essentially symmetric flare that
lasted ~6 hours in Sector 42. We fit the flare's rising and declining phases to
exponential functions. We also analysed the light curve of Sector 42 using the
Lomb-Scargle periodogram (LSP) and continuous auto-regressive moving average
(CARMA) methods. The Sector 42 light curve displayed in the present work
provides the first evidence of a strong, rapid, short-lived optical flare on
the intraday timescale in 1ES 0229+200. The variability timescale of the flare
provides the upper limit for the size of the emission region to be within
(3.3\pm0.2 - 8.3\pm0.5)x10^{15}cm. Away from the flare, the slope of the
periodogram's power spectrum is fairly typical of many blazars (\alpha<2), but
the nominal slopes for the flaring regions are very steep (\alpha~4.3), which
may indicate the electron distribution undergoes a sudden change. We discuss
possible emission mechanisms that could explain this substantial and rapid
flare.
