We have detected four flares from UV Ceti at 154 MHz using the Murchison Widefield Array. The flares have flux densities between 10--65 mJy --- a factor of 100 fainter than most flares in the literature at these frequencies --- and are only detected in polarization. The circular polarized fractions are limited to $>27$% at 3$sigma$ confidence and two of the flares exhibit polarity reversal. We suggest that these flares occur periodically on a time scale consistent with the rotational period of UV Ceti. During the brightest observed flare, we also detect significant linear polarization with polarization fraction $>18$%. Averaging the data in 6-minute, 10 MHz frequency bins we find that the flux density of these flares does not vary over the 30 MHz bandwidth of the Murchison Widefield Array, however we cannot rule out finer time-frequency structure. Using the measured flux densities for the flares, we estimate brightness temperatures between $(10^{13}-10^{14}),$K, indicative of a coherent emission mechanism. The brightness temperature and polarization characteristics point to the electron cyclotron maser mechanism. We also calculate the flare rates given our four observed flares and compare them to flare rates for the set of M dwarf stars with known 100--200 MHz flares. Our measurement is the first for flares with intensities $<100$ mJy at 100-200 MHz.
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