In 1981, John Colarusso examined typological parallels involving consonantism, focusing on the so-called laryngeals of PIE and in 1989, he published his reconstruction of Proto-Northwest Caucasian (PNWC). Eight years later, the first results of his comparative work on PNWC and PIE were published in his article Proto-Pontic: Phyletic Links Between Proto-Indo-European and Proto-Northwest Caucasian, an event which may be considered the actual beginning of the hypothesis.
Evidence
Examples of similarities that have been noted include:
A case variously named "accusative", "oblique" or "objective", marked with nasal suffixes:
PIE accusative *-m, reflected e.g. in Latinluna 'moon' (nom.) vs lunam (acc.), or Ancient Greek ἄνθρωπος (anthropos, nom.) vs. ἄνθρωπον (anthropon, acc.).
NWC: Ubykh kwæy 'well (water source)' (abs.) vs kwæyn (obl.).
References
Colarusso, John (1997). "Proto-Pontic: Phyletic links between Proto-Indo-European and Proto-Northwest Caucasian". Journal of Indo-European Studies. 25: 119–51.