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We report the discovery of millihertz quasi-periodic oscillations (mHz QPOs) from the bursting, high-inclination atoll neutron-star low-mass X-ray binary (NS LMXB) EXO 0748--676 with the Rossi X-ray Time Explorer (RXTE). This class of QPO, originally discovered in three NS LMXBs, has been interpreted as a consequence of a special mode of nuclear burning on the NS surface. Using all the RXTE archival observations of the source, we detected significant ($>3\sigma$) mHz QPOs in 11 observations. The frequency of the oscillations was between $\sim$ 5 and $\sim$ 13 mHz. We also found a decrease of the QPO frequency with time in two occasions; in one of these the oscillations disappeared with the onset of an X-ray burst, similar to what was reported in other sources. Our analysis of the X-ray colours revealed that EXO 0748--676 was in a soft spectral state when it exhibited the QPOs. This makes EXO 0748--676 the sixth source with mHz oscillations associated to marginally stable burning, and the second one that shows a systematic frequency drift. Our results suggest that the mechanism that produces the drift might always be present if the mHz QPOs are observed in the so-called intermediate state.