Can you use Gust on an opponent's Tideturner after its swap ability resolves to move it to the battlefield?

Ruling: No, you cannot use Gust after Tideturner's triggered ability resolves. Once the ability resolves and the chain is empty, there is no window to play reaction spells.

Sequence:

• Tideturner is played and its triggered ability goes on the chain
• The triggered ability is the only item on the chain
• When it resolves, the units swap positions
• The chain becomes empty
• Since the chain is empty, you stop and do not get another window to play reactions

Nuances:

• Rule 543.4 only applies when there are still items remaining on the chain after something resolves, determining whose priority comes first before the next item resolves
• Rule 544 is relevant here: when the chain is empty after resolving, you stop repeating the priority windows