Chthonic deities are the ones that live underworld, or beneath the earth, so Apollo is technically not a chthonic deity. But if you meant to ask for Apollo’s association with death, then there are some. Though, I think the prominent one would be Soranus, the Roman underworld deity, being replaced by Apollo and His cults (I’ll talk about that in the end since it’s explanation might a bit lengthy).
> Apollo is the God of tombs/cemeteries. He guards the souls in the tomb till the body decays and soul can be separated. Hermes is the god who conducts the souls to underworld, but Apollo separates the soul from the flesh. The Ionian tombs have inscriptions asking Apollo to guard the dead bodies and purify their souls.
> Apollo is the God of disease, and that’s his deadly side. He brings death to old and young alike (especially to the young boys). I know any God can bring death to a mortal if They wished, but it was under immediate care of Apollo and Artemis, and They were famously called as bringers of sudden deaths.
> Apollo is especially concerned with dead bodies and their proper burial. This can also be seen when He scolds the other Gods during Trojan war for letting Achilles drag Hector’s dead body. Apollo also protects the dead body by His magic. He is also the one to retrieve the dead body Sarpedon (a son of Zeus) from the battlefield.
> Apollo’s connection with decaying of dead bodies can also be taken from Apollo’s punishment to Python. Python means “rotter”, and the first ever punishment given by Apollo is rotting. His epithet, Pythios, also derives it’s origin from this feat of His.
> The cycle of life and death is a part of Apollo’s nature. His visit to Hyperborea brings winter to the world (and was considered as His “annual death” in Delphi.) He brought death to everything (vegetation especially)with His departure. With His return, new life would be generated. Through the summer and winter cycle He caused, Apollo was both the bringer of life and death.
> Apollo has “consumed” some Gods. I mean, Python was considered as an oracular deity so Apollo basically killed a deity and established His own cult there. And Python wasn’t the only one. Apollo also replaced Paean, an early Greek deity of healing (Paean is now only an epithet of Apollo). Hyacinthus was a pre-hellenic God as well, whose cults were consumed by cults of Apollo, or rather, both were merged and considered as one God - Apollo Hyacinthus. And the most interesting one - Soranus, a Roman underworld deity, was also subsumed by Apollo (Here He is called Apollo Soranus). Hence Apollo basically has taken over the chthonic responsibilities of the former deity - death and purification.
