Nier Replicant is filled with side tasks that players can perform during the game. The Lost Eggs Quest is a side quest from Part 1 that you can get from a merchant in the village.
If you want to complete this task, you must complete it in the first part, you will not be able to get it when you move to the second part of the game. For the Lost Eggs task, the merchant asks you to track down the chicken eggs.
The chickens lay eggs in unusual places and it’s up to you to track one. If you ask around the city, you can get some general clues, or you can simply get your eggs according to the map below.
Eggs can be found next to a pillar near the fountain west of the library. There will be no indicator that it is there until you approach, so go up to the area and then an organ arrow will appear when you are quite close.
Interact with the area to catch the eggs, then bring them back to the merchant. When you bring him an egg, he will give you a Healthy Salvo as a thank you.