GEMARA

(R. Chiya bar Avin): A person should always be quick to do a Mitzvah. Because Lot's older daughter preceded (having Bi'ah with Lot) one night before her sister, she merited that her descendents entered Yisrael four generations earlier.

Pesachim 4a - Question: Why do we check for Chametz so early (the night before)? We could check at the beginning of the sixth hour, for Chametz is not forbidden (mid'Oraisa) until the end of six hours!

Answer: We check early, for Zerizin Makdimim l'Mitzvos (zealous people do Mitzvos right away).

Rejection: If so, it would suffice to check (earlier) in the morning!

(Beraisa): "Uva'Yom ha'Shmini Yimol" - one may circumcise any time during the day, but Zerizin Makdimim l'Mitzvos - "va'Yashkem Avraham ba'Boker!"

RISHONIM

The Rif and Rosh (Pesachim 1b and 1:1) bring the Gemara in Pesachim.

Rambam (Hilchos Ma'aseh ha'Korbanos 4:6): The entire day is Kosher for Shechitah... the entire night is Kosher for burning Chelev and limbs on the Mizbe'ach... The rule is, any daytime Mitzvah is Kosher all day, and any nighttime Mitzvah is Kosher all night. Nevertheless, Zerizin Makdimim l'Mitzvos.

POSKIM

Shulchan Aruch (OC 94:5): If one was sitting in a boat or wagon, (he may pray Shemoneh Esre sitting...)

Shulchan Aruch ha'Rav: It is best to wait until reaching his destination if he can pray there without distractions. This is not a problem of souring Mitzvos and neglecting Zerizin Makdimim, for he intends to do the ideal Mitzvah.

Shulchan Aruch ha'Rav (131:5): On Rosh Chodesh, we do not say Hallel in a mourner's house. One who prayed there should say Hallel when he gets home. The Mitzvah to say Hallel is the entire day. We say it after Shacharis only because Zerizin Makdimim l'Mitzvos.

Mishnah Berurah (220:2): One who had a bad dream should ask friends to say a text saying that it will be good. He should do so in the morning, for Zerizin Makdimim.

Shulchan Aruch ha'Rav (Kuntres Acharon 431:1): Why did Chachamim enact that everyone be Zariz and check for Chametz on the night of the 14th? They did not enact so for other Mitzvos! This is because other Mitzvos have a final time, so people will not improperly delay them. The final time for Bedikas Chametz is the end of Pesach, so it was necessary to enact a time. One who transgresses it is not just lazy. He is a transgressor!

Sha'arei Teshuvah (453:1): We permit coffee during Pesach. Nevertheless, Zerizin Makdimim to roast it before Pesach, and to inspect it before buying it for rice or other species mixed in. This is a stringency of Pesach. One will be blessed for it.

Shulchan Aruch (OC 458:1): When Erev Pesach is on Shabbos, the custom is to knead the Matzos on Erev Shabbos after midday.

Beis Yosef (DH Ein): Some say not to bake them until Yom Tov, lest one eat Matzah on Erev Pesach, or lest people see Matzah ready at the start of Yom Tov and think that baking Matzah overrides Shabbos. Rav Hai Gaon says that it is our custom to bake the Matzos before Shabbos to avoid exertion on Yom Tov that could be done beforehand. Also, this enables eating the Matzah promptly; Zerizin Makdimim l'Mitzvos. R. Yerucham says that if one delays baking them until Yom Tov, perhaps he will not eat the Afikoman, which corresponds to Korban Pesach, after midnight.

Ha'aros on Birkei Yosef (681:1): 'A Mitzvah is dear in its time' whenever it is done within the proper time. Zerizin Makdimim l'Mitzvos is a different matter.

Shulchan Aruch (YD 61:5): There is no Isur to eat meat of a Behemah before separating the foreleg, jaw and stomach (which are given to a Kohen). Nevertheless, it is a Mitzvah to separate them immediately.

Levush: This is because Zerizin Makdimim l'Mitzvos.

Shulchan Aruch (262:1): We do not circumcise until sunrise. (Rema - after dawn, one was Yotzei.) The entire day is Kosher, but Zerizin Makdimim l'Mitzvos.

Shulchan Aruch (OC 444:10): If one was on his way to circumcise his son on Erev Pesach, and remembered that he has Chametz in his house, if he can return to his house and destroy it and return to circumcise, he should do so. If not, he is Mevatel the Chametz in his heart (and goes to circumcise).

Mishnah Berurah (29, citing Magen Avraham 11): If it is after the sixth hour, he cannot be Mevatel (Chametz is Asur, so it is not his), so he destroys it first. Chametz is more stringent, for one transgresses every moment.

Rebuttal (Machatzis ha'Shekel): Also Milah one transgresses every moment!

Defense (Aruch ha'Shulchan 13): Even though one transgresses every day that he does not circumcise, during the day it does not matter when he circumcises, just Zerizin Makdimim l'Mitzvos.

Aruch ha'Shulchan (YD 265:25): The custom is to circumcise each twin by himself, with Berachos for each. Some say that it is because we do not do Mitzvos in bundles. I say that this applies to matters such as Sotos and Metzora'im, which are not obligatory to do that day, but not to Milah. We do not delay the second Bris, for Zerizin Makdimim l'Mitzvos.

Kitzur Shulchan Aruch (60:7): L'Chatchilah, Birkas ha'Chamah should be at sunrise, for Zerizin Makdimim l'Mitzvos. It is best to do so amidst many people, for "b'Rav Am Hadras Melech." One should not delay for this, for Zerizin Makdimim overrides "b'Rav Am."

Kitzur Shulchan Aruch (97:9): L'Chatchilah, one says Kidush Levanah on Motza'ei Shabbos, when he is wearing nice clothes, unless Motza'ei Shabbos will be more than 10 days after the new moon, or if there is concern lest he be unable to Mekadesh the moon. It is best to do so amidst many people, for "b'Rav Am Hadras Melech." One should not delay for this, for Zerizin Makdimim l'Mitzvos overrides "b'Rav Am."

Kitzur Shulchan Aruch (130:6): When it is possible to buy Esrogim, Lulavim and Hadasim before Yom Kipur, meticulous people do so, for Zerizin Makdimim l'Mitzvos. Also, this dear Mitzvah adds to one's merits.