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You can play an early stage barathu, as that's what the racial traits in Alien Archive describe. Early stage barathu have the Early Stage Adaptation trait, the rules for which are in the stat block on the previous page.
As the chronicle says, follow the other rules for character creation in the Core Rulebook.
The chronicle doesn't actually list any rulebooks "below" the barathu section as stated, but the rulebook on the Additional Resources list that gives barathu statistics is Alien Archive, so you must bring a legal copy of that book when playing your barathu character.