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The identification of high-redshift massive galaxies with old stellarpopulations may pose challenges to some models of galaxy formation. However, tosecurely classify a galaxy as quiescent, it is necessary to exclude significantongoing star formation, something that can be challenging to achieve at highredshift. In this letter, we analyse deep ALMA/870um and SCUBA-2/450um imagingof the claimed "post-starburst" galaxy ZF-20115 at z=3.717 that exhibits astrong Balmer break and absorption lines. The far-infrared imaging reveals aluminous starburst located 0.4+/-0.1 arcsec (~3kpc in projection) from theposition of the rest-frame ultra-violet/optical emission, with an obscuredstar-formation rate of 100 Mo/yr. This star-forming component is undetected inthe rest-frame ultraviolet but contributes significantly to the lower angularresolution photometry at restframe wavelengths >3500A, significantlycomplicating the determination of a reliable stellar mass. Importantly, in thepresence of dust obscuration, strong Balmer features are not a unique signatureof a post-starburst galaxy and are indeed frequently observed ininfrared-luminous galaxies. We conclude that the ZF20015 system does not pose achallenge to current models of galaxy formation and that deep sub-/millimeterobservations are a prerequisite for any claims of quiescence. Themulti-wavelength observations of ZF20115 unveil a complex system with anintricate and spatially-varying star-formation history. ZF20115 demonstratesthat understanding high-redshift obscured starbursts will only be possible withmulti-wavelength studies that include high-resolution observations, availablewith the JWST, at mid-infrared wavelengths.

An imperfectly passive nature: Bright sub-millimeter emission from dust-obscured star formation in the z=3.717 "passive" system, ZF20115