The Greek lexicon is known for its significant proportion of words lacking a clear etymology. Previous attempts to explain these words range from the socalled “Pelasgian” hypotheses, which resort to an unattested satem Indo-European language, to Beekes’s (2010; 2014) non-Indo-European “Pre-Greek”. In this paper, we reconsider this long-disputed question, and adduce Latin and even Proto- Romance data to unveil a centum language which possibly served as the basis for borrowing in both Common Greek and, at a later date, Common Italic. We analyse several dozen difficult Greek and Italic words as borrowings from this newly identified language, for which we provide a set of phonetic laws that model its development from Proto-Indo-European. Important methodological strengths of our proposal include the systematic correspondence between Greek and Italic forms, the semantic plausibility of our etymologies, and their consistency with what is known about Proto-Indo-European word-formation patterns. Moreover, a computer implementation of these phonetic laws ensures its formal consistency and validates the chronological ordering we put forward. This is all the more important since most of our etymologies involve more than one of these phonetic laws, which is an additional confirmation of the plausibility of our proposal.