Do I loose æmber after plaing Full Moon, then Chota Harzi?
The active player (presumably you) chooses the order. The result is likely that you choose to end up with 1 æmber.
The Full Moon effect trigger and Chota's play trigger both happen when you play the card, at the same time. As such, the active player chooses the order they resolve in. Unless you're somehow doing this on your opponent's turn, you'll get to choose which comes first, and thus whether or not you end up with the æmber.
From the rules, page 9:

ACTIVE PLAYER
The active player is the player taking the current turn. The active player makes all necessary decisions for all card abilities or timing conflicts that need to resolve during their turn.