Chiltis is a root vegetable known as Asafetida1,2, which is like garlic and is considered extremely strong and used in India for cooking and medicine. It is called חלתית from the root חוֹלֶה, sick, because it makes one sick (supposedly burns a hole in one's stomach if not careful3).
It is mentioned in the Mishna in Avodah Zara 35B, where it listed as one of the items one may not purchase from non-Jews. Rashi:
חלתית - מין פירי הוא שקורין לזר"א4 בלע"ז ומחתכין את קרטיו בסכין ואסור
משום שמנוניתא דסכינא
It appears in halachic discussion as an extreme case for sharpness; something sharper than onion or garlic, and therefore some opinions, such as the Maharam M'Rottenburg, hold that only it is mechalia l’shvach - refreshes taste in a pleasant way, not t'znon etc.
Similarly, in many cases where we say that a davar charif (something spicy/sharp) is not boleya kula (see SH YD Siman 96:1) or mechalia l’shvach (such as with lemon and salt in SH YD Siman 96:3,4), chiltis is listed as an exception, given how extremely sharp it is.
1 - Wikipedia article (warning: contains swear words)
2 - Klein dictionary entry
3 - See page 23 of this OU article
4 - Otzar Laazei Rashi entry