After your battle at the Lifemend Stump, Galfrid needs you to gather some eggs.
This quest is only available if you started the game in Gridania, you have completed the quest Chasing Shadows, and have reached level 7.
Starting the Quest
To start the quest, talk to Galfrid in the Central Shroud.
Obtain Chigoe Egg Sacs
The locations of Chigoes will be marked on your minimap, and the general area will be marked in red on the main map. Go to that area and kill Chigoes until the duty list (under the minimap by default) shows that you have collected three egg sacs.
Deliver the Chigoe Egg Sacs to Monranguin
After you have gathered the egg sacs, look for the green checkmark on the map and minimap. Go there and talk to Monranguin to hand over the egg sacs and complete the quest.
Next Main Scenario Quest
After completing the quest, you will need to be at least level 8 to proceed to the next quest. After you reach level 8, talk to Monranguin to accept the next quest: Surveying the Damage.