While the evidence for the o-stem thematic genitive singular in the earliest-attested Ancient Greek fairly clearly reflects inherited Core-Indo-European *-osi̯o (Mycenaean °o-jo, Homeric -οιο, cf. Vedic -asya, Old Avestan -ahiiā, Very Old Latin -osio, etc.), the continuity of the Classical Greek genitive singular ending -ου (Attic-Ionic), -ω (West Greek and other dialects with Doris seuerior vocalism) is less certain. The two main proposed candidates have been either a continuation of inherited *-osi̯o > -οιο > -oυ/-ω (with loss of intervocalic -i̯- and contraction) or an analogical replacement of the inherited genitive with a pronominal genitive singular ending *-e-so (cf. Hom. τέο, Goth. ƕis, OCS česo, etc.) → *-o-ho > -oυ/-ω (with loss of intervocalic -h- and contraction). In this paper I will critically review the main advantages and disadvantages afforded by either hypothesis and weigh them against the evidence from the first-millennium Ancient Greek dialects to determine whether one or the other solution can better explain the data for the thematic o-stem genitive singular -oυ/-ω as actually attested in epichoric Ancient Greek dialectal inscriptions.