CUORE, an array of 988 TeO[Formula: see text] bolometers, is about to be one of the most sensitive experiments searching for neutrinoless double-beta decay. Its sensitivity could be further improved by removing the background from [Formula: see text] radioactivity. A few years ago it was pointed out that the signal from [Formula: see text]s can be tagged by detecting the emitted Cherenkov light, which is not produced by [Formula: see text]s. In this paper we confirm this possibility. For the first time we measured the Cherenkov light emitted by a CUORE crystal, and found it to be 100 eV at the [Formula: see text]-value of the decay. To completely reject the [Formula: see text] background, we compute that one needs light detectors with baseline noise below 20 eV RMS, a value which is 3-4 times smaller than the average noise of the bolometric light detectors we are using. We point out that an improved light detector technology must be developed to obtain TeO[Formula: see text] bolometric experiments able to probe the inverted hierarchy of neutrino masses.