I often talk about how ‘chthonic’ isn’t really a meaningful thing to say (cf. Polinskaya 2013: 63-64 edited to add: I am certainly not alone in this thought, a lot of scholars, not just Polinskaya and me, talk about this!). It doesn’t really appear to have the same weight of meaning in the ancient world as it does now. It doesn’t have any malefic connotation (usually), and it usually just means ‘in or under the ground’. Anyway, there are a few instances in which ancient authors directly discuss divine distinctions, and here is a (very short) discussion of one such instance, from Isokrates’ To Philip, in which he says:
ἀλλὰ καὶ τῶν θεῶν τοὺς μὲν τῶν ἀγαθῶν αἰτίους ἡμῖν ὄντας Ὀλυμπίους προσαγορευομένους, τοὺς δ᾽ ἐπὶ ταῖς συμφοραῖς καὶ ταῖς τιμωρίαις τεταγμένους δυσχερεστέρας τὰς ἐπωνυμίας ἔχοντας, καὶ τῶν μὲν καὶ τοὺς ἰδιώτας καὶ τὰς πόλεις καὶ νεὼς καὶ βωμοὺς ἱδρυμένους, τοὺς δ᾽ οὔτ᾽ ἐν ταῖς εὐχαῖς οὔτ᾽ ἐν ταῖς θυσίαις τιμωμένους, ἀλλ᾽ ἀποπομπὰς αὐτῶν ἡμᾶς ποιουμένους.
In the case of gods too I observe that those who bring men blessings are called Olympians, while those responsible for calamities and punishment have less pleasant names; private individuals and cities have founded temples and altars of the one group, while the other is honoured neither in sacrifices nor in prayers, but we perform rites of expulsion against them. (Isok. 5. 117; trans. Parker.)
The term Isokrates uses is ἀποπομπή, and indicates expulsion rites. Harpokration, the second-century CE lexicographer, references Isokrates’ use of the term in his entry of ἀποπομπας, and comments that Apollodoros dedicated a book of his treatise Concerning the Gods to ἀποπομπαῖοι, the ‘sending away gods’ or ‘gods of aversion’, and this presumably focused on expulsion rites. Pausanias tells us about an altar at Titane dedicated to Ἀποτρόπαιοι. The ἀποτρόπαιοι turn evils away of their own accord, and likewise ἀποπομπαῖοι lead evils away, rather than forcibly expelling them. Isokrates is not necessarily referring to ‘nameless’ gods having rites of expulsion performed ‘against them’, but rather that the divinities are viewed as being complicit in the expulsion of evils from the city. This does not refer to ‘major’ Underworld or agrarian gods, like Hades, Persephone, or Demeter. It could refer to the Erinyes, but Isokrates would have been familiar with Aischylos’ Eumenides, in which the Erinyes are welcomed into Athens and honoured, rather than expelled. Furthermore, this would be far from a wholesale commentary on the nature of Olympic versus chthonic divinities. What Isokrates might be commenting on is less a form of ‘divinity proper’ and so could be daimons, or even heroes. ‘Special’ categories of the dead were referred to as ἀνώνυμοι (‘nameless’) and negative modifiers like this were frequently used to characterise the dead and the Underworld. The dead, and particularly ‘special’ dead and heroes were ‘chthonic’ by definition, and were used by the living for their own benefit, for example with the delivery of katadesmoi.
 Nock 1986: 600; cf. Norlin 1928: 316.
 cf. Laistner 1927: 162
 J.E. Harrison comments that the closest we might come to understanding these rituals is through modern ceremonies of exorcism, but without the magical connotation and the ‘degraded superstition’ (Harrison 1903: 8).
 Harpokrat. s.v. ἀποπομπας. ‘‘Ισοκράτης Φιλίππῳ. ἀποπομπαῖοί τινες ἐκαλοῦντο θεοί, περὶ ὧν ‘Απολλόδωρος ἐν ς’ περὶ θεῶν διείλεκται’.
 Paus. 2.11.1.
 For more on the ‘special dead’ see Garland 1985: 77-103
 Henrichs 1994: 55
 Faraone 1991: 3, 22 n. 26; Larson 1995: 118
If you like what I do here, and on YouTube and Twitter, you can buy me a coffee.