If Chained to the Rocks leaves the battlefield before its triggered ability resolves, the target creature won't be exiled.

Chained to the Rocks's ability causes a zone change with a duration, a style of ability introduced in Magic 2014 that's somewhat reminiscent of older cards like Oblivion Ring. However, unlike Oblivion Ring, cards like Chained to the Rocks have a single ability that creates two one-shot effects: one that exiles the creature when the ability resolves, and another that returns the exiled card to the battlefield immediately after Chained to the Rocks leaves the battlefield.

The exiled card returns to the battlefield immediately after Chained to the Rocks leaves the battlefield. Nothing happens between the two events, including state-based actions.

Auras attached to the exiled creature will be put into their owners' graveyards (unless they have bestow). Equipment attached to the exiled creature will become unattached and remain on the battlefield. Any counters on the exiled creature will cease to exist.

If a creature token is exiled, it ceases to exist. It won't be returned to the battlefield.

If the land Chained to the Rocks is enchanting stops being a Mountain or another player gains control of it, Chained to the Rocks will be put into its owner's graveyard when state-based actions are performed.

In a multiplayer game, if Chained to the Rocks's owner leaves the game, the exiled card will return to the battlefield. Because the one-shot effect that returns the card isn't an ability that goes on the stack, it won't cease to exist along with the leaving player's spells and abilities on the stack.