Falling star to a might 3 unit with zhonya

Yes — the unit dies. Zhonya's only saves it from the first of Falling Star's two damage triggers; the second trigger kills it afterward.

Sequence: Falling Star resolves and creates two separate "deal 3" triggers on the Chain. The first trigger deals 3 damage to the Might 3 unit. In Cleanup, it would die, so Zhonya's is killed instead — the unit is healed to full, exhausted, and recalled to base. The second trigger then resolves, dealing 3 damage to the unit at base, which is lethal (3 damage ≥ 3 Might), and it dies.

Note this only works because Falling Star has no "at a battlefield" restriction, so the unit at base is still a legal target. If Zhonya's is face-up it saves the first death automatically; if it's Hidden, you can choose when to reveal it, but it still won't stop the second trigger.