The preferred way to light on Chanukah is with olive oil, because it was used in the Bet Hamikdash. Today, we find some olive oils made expressly for lighting, labeled "Not fit for human consumption." Is it permissible to light with these oils?
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) discusses a certain olive oil that is too bitter to eat. He rules that it is still fit for the misva, as long as there is no ruach tuma on it; e.g. it wasn't left under a bed. Rav Haim Kanievsky, as quoted by Rav Nissim Korelitz, ruled that the oil labeled "not fit for human consumption" is no different from the bitter oil permitted by the Ben Ish Hai. Although, one could distinguish between the two and say that, technically, the bitter oil is edible; people just avoid it because of its taste. On the other hand, the other oil is very acidic and would be dangerous for anyone to eat it. However, they don't make that distinction.
Rav Eliashiv zt"l (Ashrei Ish p. 239), ruled that it is clearly better to use edible olive oil for the misva, since the oil used in the Bet Hamikdash was edible.
Some claim that even oils labelled "not fit for human consumption," are indeed edible. They mark it as such to avoid paying the higher import tariff for foodstuff.
SUMMARY
Lechatehila, it is preferable to use olive oil that is fit for human consumption. However, any olive oil, even if it is "not fit" or bitter, is kosher for Chanukah lighting. (Yalkut Yosef, Chanukah p.117)
