Nier Replicant is filled with side quests that players can complete as they play through the game. The Lost Eggs Quest is a Part 1 side quest that you can get from the shopkeeper in the village.
If you want to complete this quest, you need to finish it in part one, you won’t be able to get it when you move into part two of the game. For the Lost Eggs quest, the shopkeeper will ask you to track down a chicken egg.
The chickens have been laying their eggs in unusual places, and it is up to you to track one down. If you ask around town, you can get some general clues, or you can simply follow the map below to get your egg.
You can find the egg beside on of the pillar near the fountain to the west of the library. There will be no indicator that it is there until you get very close, so walk up to the area and then an organ arrow will appear when you are pretty much right on top of it.
Interact with the area to grab the egg, then bring it back to the shopkeeper. When you bring him back the egg, he will give you a Health Salve as a thank you.