If my opponent moves a 1/1 unit to a battlefield and passes priority, then I play Hextech Ray to deal 3 damage to it, is there any window where they could play Primal Strength to save the unit?

Ruling: No, there is no window to play Primal Strength to save the unit in this scenario. Once the opponent passed focus to you without playing an action, they cannot respond to your Hextech Ray with an action. The unit will die when Hextech Ray resolves.

Sequence:

• Opponent moves unit and passes focus without playing actions
• You play Hextech Ray (starting a chain)
• Opponent cannot play Primal Strength (actions cannot be used as reactions)
• Chain resolves and unit dies from Hextech Ray damage
• After the chain resolves, focus automatically passes back to opponent
• Opponent could now play Primal Strength, but it's too late to save the unit

Nuances:

• You can never react with an action - only reactions can be played in response to a chain
• Focus automatically passes after each chain resolves, but this automatic passing does not count toward "both players passing"
• Units die as soon as lethal damage resolves, not after all chains resolve
• The opponent's only chance to save the unit was to play Primal Strength before passing focus initially