Samples of material returned from the Moon have established that widespread lunar volcanism ceased about 3.2Gyr ago. Crater statistics and degradation models indicate that last-gasp eruptions of thin basalt flows continued until less than 1.0Gyr ago, but the Moon is now considered to be unaffected by internal processes today, other than weak tidally driven moonquakes and young fault systems. It is therefore widely assumed that only impact craters have reshaped the lunar landscape over the past billion years. Here we report that patches of the lunar regolith in the Ina structure were recently removed. The preservation state of relief, the number of superimposed small craters, and the `freshness' (spectral maturity) of the regolith together indicate that features within this structure must be as young as 10Myr, and perhaps are still forming today. We propose that these features result from recent, episodic out-gassing from deep within the Moon. Such out-gassing probably contributed to the radiogenic gases detected during past lunar missions. Future monitoring (including Earth-based observations) should reveal the composition of the gas, yielding important clues to volatiles archived at great depth over the past 4-4.5Gyr.