On this page of our guide to Psychonauts 2 you can view the locations of Supply Chests appearing in Green Needle Gulch.
There are two Supply Chests in this level.
Supply Chest 1
Location Compton's Menagerie.
You will come across this chest while exploring the area on the right, next to a huge mountain. The collectible can be seen from a distance.
Supply Chest 2
Location Cassie's Hives.
You will come across this Chest while exploring Cassie's house, specifically in her bedroom.