Gemara

Rav Papi permitted bakers of the Reish Galusa's house to thicken a Tavshil with Chasisi.

Version #1 - Rava: Does one permit such a matter in a place where slaves [who are not careful about Mitzvos] are found?!

Version #2: Rava himself thickened a Tavshil with Chasisi.

35a (Mishnah): One is Yotzei with Matzah of wheat, barley, Kusmin, Shiboles Shu'al or Shifon.

Inference: One is not Yotzei with rice or millet.

(Reish Lakish): "Lo Sochal Alav Chametz Shiv'as Yomim Tochal Alav Matzos" - Matzah must be made from something that can become Chametz. Rice and millet cannot become Chametz. They merely decay.

Our Mishnah is unlike R. Yochanan ben Nuri;

(Beraisa - R. Yochanan ben Nuri): Rice is a grain. If it became Chametz one is Chayav Kares for eating it on Pesach. One may be Yotzei with rice Matzah;

114b (Beraisa - R. Yosi): It is a Mitzvah to bring Chazeres, Charoses and two cooked foods.

(Rav Huna): Even beets and rice may be used.

Rava strove to use beets and rice, because Rav Huna said so.

Inference (Rav Ashi): No one is concerned for the opinion of R. Yochanan ben Nuri.

Rishonim

Rambam (Hilchos Chametz 5:1): There is no concern for Chametz with rice, millet beans, lentils and similar things. Even if one kneaded a dough of rice flour or similar matters in boiling water and covered it with garments until it inflated like a dough that fermented, one may eat it during Pesach. This is not Chimutz, rather, spoilage.

R. Mano'ach: Sefer ha'Minhagos says "the entire world does not eat seeds during Pesach, because they become Chametz. This is why they are called Chimtzi." It is unreasonable to say that the custom is based on Isur. No Kitniyos become Chametz! Rather, it is not normal to eat Kitniyos during the festival, for there is a Mitzvah of Simchah, and there is no Simchah in a Tavshil of Kitniyos. Afterwards, I found written that there is a species called Vitzash that is from wheat kernels that have different forms in the ground [unlike normal wheat], e.g. Zunin. In a year that is not blessed, the grain sprouts abnormally. The word "Zunin" is based on "Tizneh ha'Aretz" (an expression of harlotry). In a year of much rain, Vitzash grows normally, and it is called Vitzash Farmentals. Therefore, they forbade all Kitniyos. This reason has a source.

Bi'ur Halachah (DH v'Yesh): R. Mano'ach's first reasons for the custom are flimsy. He concluded that there is a species of wheat that in dry years, the kernels look like seeds, therefore they forbade all kinds of seeds.

Mordechai (588): Based on the Rambam, we can permit rice. The Aruch says that this is Orez, which the Gemara permits. Even according to Rashi, who says that it is millet, it is not one of the five grains. However, Semak supports the custom to forbid all Kitniyos during Pesach. This is not due to Chimutz. Rather, it is because grain and Kitniyos are both Ma'ase Kederah. Also, it is piled up, like grain (Bava Metzi'a 88b). They can be confused. Also, in some places they make bread from Kitniyos like from the five grains. People who are not Bnei Torah can confuse them. They are unlike Yerakos (vegetables in which one eats the plant itself) such as cabbage, Kerishin (big onions), and similar things. They are not like grain at all. These would not be confused. It is a proper custom to avoid all Kitniyos. It is proper to forbid pulse and mustard, for these are piled up. The Gemara permits even rice, for in those days, all were experts in laws of Isur v'Heter. Nowadays we decree. Rav Sadya Gaon similarly distinguished between nowadays and previous generations regarding one who gave birth amidst Zivah (seeing non-menstrual blood). We should forbid even putting them in boiling water, lest one put them in cold water. R. Baruch and R. Shimshon of Ivra did not eat Kitniyos during Pesach, but R. Yechiel ate white beans.

Tosfos (40b DH Rava): The Ri says like the Aruch, that Chasisi is lentil flour, which do not normally ferment so much.

Poskim

Shulchan Aruch (OC 453:1): Rice and other kinds of Kitniyos do not become Chametz. One may make a Tavshil (cooked food) from them.

Rema: Some forbid. The custom in Ashkenaz is to be stringent, and one may not deviate.

Beis Yosef (DH v'Yesh): This is an excessive stringency. Also R. Yerucham (55:3 41a) says that it is a foolish custom, unless they do so to be stringent on themselves. I do not know why.

Beis Yosef (DH uv'Hagahos, citing Hagahos Maimoniyos): Semak says that R. Shmuel of Ivra and others forbid eating during Pesach Kitniyos such as beans and lentils, but R. Yechiel and other Gedolim permit. It is very hard to permit, for others consider it Isur. They do not err to forbid due to Chimutz. Even children know that only the five grains become Chametz. The Gemara explicitly says so. Rather, grain and Kitniyos are both Ma'ase Kederah. Kitniyos can be confused with porridge. Also, sometimes grain is mixed in [with Kitniyos], and one cannot separate it well.

Beis Yosef (ibid.): Only Ashkenazim are concerned for this.

Taz (1): The Tur says that it is because wheat gets mixed with them. Semak says that a Kitniyos dough can be confused with a dough of Chametz. This is a mere stringency. One should not deviate, for this is the custom.

Gra (DH v'Yesh): A support for the custom is 40b. See Tosfos (DH Rava). Even though lentils are Kitniyos, [in Version #1] Rava forbids lest they be confused [with grain]. All the more so nowadays [that many are not careful about Mitzvos] one should be stringent.

Mishnah Berurah (6): There are commoners and ignoramuses who would not distinguish between flour and bread of Kitniyos and that made from grain. Therefore, they forbade all bread and Tavshilim [of Kitniyos]. One may not even cook whole rice and Kitniyos, for we do not distinguish. Also, perhaps there are grain seeds among them.

Kaf ha'Chayim (10): Mor u'Ktzi'ah says that his father wanted to abolish this inferior custom. The stringency leads to transgression! People cannot eat Kitniyos for satiation, so they must bake much Matzah, especially Aniyim, and they are not careful enough with the dough. They are close to come to an Isur Kares! Besamim Rosh (348) says that it is a mistaken custom. The Pri Chodosh supported the custom. We [Sefardim] are stringent only about rice. One year, after it was checked three times, a wheat kernel was found inside. From then on, we do not eat it. Also the Chida says so, but that we do not protest against one who eats it. In particular, it is a staple food for Aniyim and children in Yerushalayim. Pekudas Elazar says that now also Sefardim in Yerushalayim do not eat Kitniyos. However, nowadays there are many Kehilos in Yerushalayim. Each keeps its custom. Some eat Kitniyos during Pesach, and some do not. This is not Lo Sisgodedu, since each is a Kehilah by itself.

Mishnah Berurah (7): One may not be lenient even on the last day of Pesach. In any case, in pressed circumstances, if one has nothing [else] to eat, he may cook anything except for the five grains. Even then, Kitniyos are better than rice, millet and Ratzka (see Igros Moshe below), which more resemble the five grains, so there is more reason to decree about them.

Igros Moshe (YD 2 25 DH uv'Davar): What we call Kasha, which was called Ratzka in Europe, is not Kusmin (spelt). Rather, it is a kind of Kitniyos, and not grain. One blesses Borei Peri ha'Adamah if the Pri is recognized, and if not, sheha'Kol.

Mishnah Berurah (7): Surely, the same applies to a Choleh (sick person), even if there is no danger. One may cook Kitniyos for him, but he must check and separate very well to ensure that there are no grain seeds mixed in. The Chasam Sofer (Teshuvah 122) and Chayei Adam say that even when one can be lenient, l'Chatchilah he should scald them in boiling water. Whatever we can fix, we fix.

Kaf ha'Chayim (13): In pressed circumstances in a famine year, if poor people lack what to eat, Sedei Chemdah brings two opinions, and concludes like the lenient opinion, but only for Aniyim, for what is absolutely essential.

Rema (ibid.): Surely we do not forbid b'Di'eved if they fell into a Tavshil.

Gra (DH Mihu): We do not decree about this, and there is no custom [to forbid].

Mishnah Berurah (8): If one sees Kitniyos kernels in the mixture, he must discard them.

Mishnah Berurah (9): There must be a majority of Heter. If not, it is not called a mixture. It is like eating pure Kitniyos.

Rema (ibid.): One may leave Kitniyos in the house.

Magen Avraham (3): Likewise, one may benefit from them. Yesh Nochlin says that it is good to be stringent not to eat cumin or dill until the last day, for it is impossible to separate them well.

Note: If an animal ate Chametz, its meat, milk, or eggs are not Chametz. (In some cases, we say that one who ate them benefited from Chametz, but he did not eat Chametz.) However, some say that if bacteria (too small for the eye to see) ate Kitniyos (e.g. corn syrup) and produced sugar, it is as if the Kitniyos changed form by itself, and the sugar is considered Kitniyos, just like whiskey is absolute Chametz.

Rema (ibid.): Seeds of cumin and dill are not Kitniyos. One may eat them during Pesach.