Mikestackpole's Comments

Got mine at 48, 57 during a Time Rift. Found another in roughly the same spot that had appeared during a Rift, but persisted after it. Trying to battle it during the Time Rift is tough since you can get attacked while pet battling. If so, just jump back in. The cub will be healed and your pet won't, but it can still work.

At the point mentioned, you pick up an acorn (glowing purpLe). For the next 3-4 minutes you can feed an animal hunting for acorns.  As luck would have it, just west of where you got the acorn, there is an "acorn harvester" just hanging out atop a rock. Click on him, and you'll create Chestnut!