We report the serendipitous discovery of a bright galaxy (Gal-A) observed as part of the ALMA Large Program to INvestigate [CII] at Early times (ALPINE). While this galaxy is detected both in line and continuum emission in ALMA Band 7, it is completely dark in UV/optical filters and only presents a marginal detection in the UltraVISTA Ks band. We discuss the nature of the observed ALMA line, i.e. whether the emission comes from [CII] at z~4.6, or from high-J CO transitions at z~2.2. In the first case we find a [CII]-to-FIR luminosity ratio of log(L_[CII]/L_FIR)=-2.5, consistent with the average value for local star-forming galaxies (SFGs); in the second case, instead, the source would lie outside of the empirical relations between L_CO and L_FIR found in the literature. At both redshifts, we derive the star-formation rate (SFR) from the ALMA continuum, and the stellar mass (M*) by using stellar population synthesis models as input for LePHARE spectral energy distribution (SED) fitting. Exploiting our results, we believe that Gal-A is a Main-Sequence (MS), dusty SFG at z=4.6 (i.e. [CII] emitter) with log(SFR/[M/yr])~1.4 and log(M*/M)~9.7. This work underlines the crucial role of the ALPINE survey in making a census of this class of objects, in order to unveil their contribution to the global star-formation rate density (SFRD) of the Universe at the end of the Reionisation epoch.