Is there ever an opportunity to start a chain on an opponent's turn?

Ruling: You cannot start a chain on your opponent's turn. You can only play things in response to your opponent starting a chain.

Nuances:

• Playing a champion to a battlefield does not create a window for response
• Moving a champion from base to an already-owned battlefield and passing turn does not create a window for response
• If a unit triggers an ability as it enters play, a chain begins and items can be added onto that chain
• When moving a unit to an uncontested battlefield, this triggers a noncombat showdown where the non-attacking player can eventually get priority to play cards