Being that llamas are ruminates it seems to me that they clearly chew their cud. But I have not found any definitive information on whether or not the have fully split hooves. Furthermore, they are not in the list of animals with one sign in Vayikra 11:4-7. Can anyone clarify this matter?
Llamas are members of the Camelidae family, and as such do not have split hooves, only two large toenails, as well as a soft padding behind them. An essential element in an animal being kosher is having split hooves, and hence are not kosher. As members of the camelid family there are presumably included in the verse under the general category of camels, all of whom are pseudoruminants with three-chambered stomachs.
Besides the answer from @Jewels we have the answer from impure animals: present, future, past which actually mentions the llama specifically. The comment is
Interesting explanation from a comment here: Gamal, Shafan, Arnevet are written in the Torah in the three tenses (past, present, future) and so refer to Bactrian camels (past, where Avraham came from), dromedaries (present, where Bnei Yisrael were) and llamas and relations (future, to be discovered after 1492). – Michoel Apr 5 '13 at 6:34
I also dealt with this on mail-Jewish Volume 33 Number 61
From: Hillel (Sabba) Markowitz
Date: Tue, 12 Sep 2000 23:36:38 -0400
Subject: Re: Rabbits and Camels
The term "maalai gairah" does not necessarily mean a ruminant. It is an interesting point that a fiction book (Watership Down) pointed out what many veterinarians did not know but which turned out to be correct, that rabbits "rechew" their food even though they do not have the extra stomachs that true ruminants do.
An article in from the Association of Orthodox Jewish Scientists suggested a different translation. It suggested a possibility based on the tense of the verb used in "splitting the hoof". I keep forgetting which kind of camel (one or two humped) had existed in the time of Avraham but disappeared from that area by Yetzias Mitzrayim but I think it was the two humped camel. That leads to
Two humped camel - upharsa lo hifrisah - past tense
One humped camel - uses mafris - present tense
llama - uses yafris - future tense not discovered until "modern" times.
While I don't know if this is correct or not, it certainly is an intriguing thought.
I understand from https://en.wikipedia.org/wiki/Llama that the llama is a member of the camel family and so is not kosher.