ביצה שנולדה בי"ט אסור ליגע בה: הגה (דהיינו לטלטלה) (מרדכי ריש ביצה ופ' כל הכלים) וכל שכן שלא לאכלה ואם נתערבה אפי' באלף כולן אסורות:

An egg laid on Yom Tov is forbidden to touch Rema: meaning to handle (Mordechai, beginning of Beitzah and ch. Kol HaKelim) and certainly not to eat. If it became mixed with others, even with a thousand, all are forbidden.

If there is doubt whether it was laid on Yom Tov or on a weekday, it is forbidden.

An egg laid on Yom Tov that was inadvertently cooked together with meat and a stew — if there is sixty times its volume in the mixture, everything is permitted except the egg itself. But if the stew was clarified by it or something similar — something that affects appearance and taste — it is not nullified.

It is permitted to invert a vessel over it so it does not break, provided the vessel does not touch it.

If it was laid on the first day of Yom Tov it is permitted on the second day of Yom Tov in the two days of Diaspora holidays. But for the two days of Rosh Hashanah, and similarly for Shabbat and Yom Tov that are adjacent to each other — if it was laid on one it is forbidden on the other. Rema: If Yom Tov falls on Sunday and Monday and the egg was laid on the preceding Shabbat, it is permitted on the second day of the Diaspora holiday. (Maharil)

An egg that emerged mostly before Yom Tov and then went back in and was afterward laid on Yom Tov — it is permitted. Therefore, even if one checked a hen's nest just before nightfall on the eve of Yom Tov and found no egg, and the next morning got up early and found an egg — it is permitted, since hens do not lay at night and we assume the greater part had already emerged the day before and went back in. This applies when there is a rooster within sixty houses with no river without a bridge separating them, for otherwise it is possible she laid at night and it would be forbidden. But if one did not check before Yom Tov, even if there is no rooster with her it is permitted, since we assume it was laid the day before — and without a rooster most hens lay during the day. Therefore it is permitted to buy eggs from a non-Jew on the first night of Yom Tov, as we assume they were laid on the eve of Yom Tov. Similarly on the second night of the two Diaspora Yom Tov days — but not on the second night of Rosh Hashanah, nor on the night of Yom Tov that follows Shabbat. Rema: A non-Jew who casually mentions that the eggs were laid yesterday may be relied upon. (Mordechai, beginning of Beitzah) This applies specifically to Yom Tov that falls in the middle of the week, but Yom Tov that falls on Sunday — where there is concern the egg was laid on Shabbat and is Biblically forbidden on Yom Tov — a non-Jew speaking casually is not believed. This applies only to the first day of Yom Tov, but on the second day, even Rosh Hashanah, he is believed since the prohibition is only Rabbinic. (Terumat HaDeshen §79)

One who slaughters a hen and finds fully formed eggs inside — they are permitted, even on Yom Tov that follows Shabbat.

A chick hatched on Yom Tov is forbidden. If it hatched on Shabbat it is forbidden on the Yom Tov that follows.