A so far overlooked sound change in the historical phonology of the Guaranian branch of the Tupi-Guarani language family is discussed in the present paper. The sound change in question, which accounts for certain synchronic morphological irregularities, consists of the insertion of the glottal fricative h in word-initial position any time the next (right-adjacent) syllable has a glottal stop ʔ as its onset consonant. Allomorphy resulting from this change is shown to affect verbal, nominal, and postpositional prefixes, as well as monomorphemic lexemes, thus unifying the treatment of synchronic patterns which are often addressed as an exclusive trait of certain verb forms. The paper ends by discussing the issue of internal classification, pointing a few limitations in past attempts to ground the subgrouping of Tupi-Guarani languages on phonological grounds, and highlighting the status of glottal prothesis as the first known phonological isogloss exclusively shared by the Guaranian varieties.