"Just a random question - do you happen to know if a portion of chthonic sacrifices was offered first to Hestia?  I had always heard that She received the first and last portion of all sacrifices, but given the difference between Olympian and Chthonic sacrifices, I have to wonder.  Any light you can shed on the question would be appreciated!"

There are records that at least in some parts of ancient Hellas, Hestia was always sacrificed to first and last in state festivals, and I have adopted that for my household worship as well; many modern Hellenists have. That said, there is a difference between rituals held for the Ouranic deities and the Khthonic; most notably for this question, in the altar used.

In ancient Hellas, an altar was called a 'bômos' (βωμός)--properly signifying any elevation--with an 'epipuron' (ἐπίπυρον)--a movable pan or brazier--used on top of the bômos so it could serve as an altar for burnt-offerings. The household hearth was used to make sacrifices as well, and thus served as an altar of sorts. It was named after the Theia of the home and hearth: 'hestía' (ἑστία). Some state-owned altars--especially when they were simply large fires--were named 'hestía' as well.

These altars were used for sacrifices to the Ouranic Theoi, but were rarely--if ever--used for sacrifices for the Khthonic Theoi. For Khthonic Theoi, an offering pit--'bothros' (βόθρος) in Greek texts--was used. Bothroi were usually dug when the occasion called for it, and closed up afterwards. As written previously, the Khthonic Theoi received special nighttime offerings of black animals, unmixed wine and special libations of milk and honey. Animal sacrifice was always done in a holókaustos--a sacrifice where the entire animal was burned and none of the meat was saved for human consumptions.

State festivals were almost always held for Ouranic deities, and they included a feast, consisting of the meat of the sacrificed animal. This wasn't possible with sacrifices to the Khthonic deities; there was no meat to feast on--and no occasion to feast. This matters, because our primary evidence on the topic is one of the Homeric Hymns to Hestia:

"Hestia, in the high dwellings of all, both deathless gods and men who walk on earth, you have gained an everlasting abode and highest honour: glorious is your portion and your right. For without you mortals hold no banquet, -- where one does not duly pour sweet wine in offering to Hestia both first and last." [XXIX]

It is my personal opinion that Hestia was not honoured (first, last or at all) in Khthonic rites. In fact, I think as few as possible Gods were called in these rites, and all of them had a Khthonic character. I think this is tied to the practice of miasma--after all, contact with the Underworld (and thus the Khthonic Gods) was a major source of it.

Within Hellenic practice, miasma describes the lingering aura of uncleanliness in regards to a person or space through which contact is made with the Gods. Next to piety, being ritually clean is one of the most important things to adhere to within Hellenismos. Miasma occurs whenever the space or person comes into contact with death, sickness, birth, sex, excessive negative emotions and bodily fluids. It also comes from a lack of contact with the Hellenic Gods. As a note, I should say that not the actual acts of dying, sex and birth cause miasma but the opening up of the way to the Underworld (with births and deaths) as well as contact with sweat, blood, semen, menstrual blood and urine.

Our Gods are immortal and are sometimes called the Deathless Ones. It's our duty to uphold this sacred name by making sure no Gods but psychopomps (guides of the dead) come in contact with death even if it's through us. If we can not respect Their purity, They might be inclined to withhold Their gifts from us. As such, I cannot even phantom inviting Hestia into a ritual with a Khthonic character.