A Chain is a stack that determines the order of resolution for activated Cards and Effects. Cards and Effects are on a Chain only if they activate.
Use of Chains
Chains are used when a Card or Effect is activated before another activated Card or Effect resolves. Each player has the opportunity to respond to each activation by activating another Card or Effect. Each activation is placed on the Chain as a Chain Link, with the first activation being Chain Link 1. Players have to follow Spell Speed 2 and Spell Speed 3 Effect Timing rules when adding Effects to the Chain.
If neither player responds to the most recent Chain Link, the Chain resolves backwards. Meaning the last Chain Link added to the Chain is resolved first.
Add while Constructing
Cards and Effects can only be added to a Chain while it is being constructed. Once a Chain starts to resolve, Cards and Effects cannot be activated until the entire Chain has resolved.
Starting a Chain
Usually, the turn player has the right to start a Chain at any time during his turn. However, this right will pass to the opponent under the following conditions:
Building a Chain
The Card or Effect that started the Chain (the first Card or Effect that has been activated) is Chain Link 1. The next is Chain Link 2, with each additional Chain Link being numbered in ascending order, with these numbers corresponding to when it was activated concerning the other Chain Links.
Cards and Effects can only be activated as a Chain Link 2 or higher if they have an equal or greater Spell Speed than the previous Chain Link. Spell Speed 1 Effects cannot be activated as a Chain Link 2 or higher, except for Trigger and Trigger-like Effects if they triggered simultaneously; in this case, they must be placed on the Chain first before either player has the opportunity to activate Spell Speed 2 and Spell Speed 3 Effects.
New Chain Links are activated in response to both the most recent activation (the immediately previous Chain Link) and the event that Chain Link 1 is responding to.
Opponent may add a Chain Link
After placing all Spell Speed 1 Effects on the Chain, or after any fast Effect activation, the player who did not add the last current Chain Link to the Chain has the right to add a new one or pass to their opponent. If their opponent then decides not to add to the Chain, the Chain is now complete. Cards and Effects cannot be resolved until the Chain is complete.
Resolving a Chain
Once both players have decided not to add to the Chain, the Chain is complete. At this time, the Chain is resolved backwards, so it starts with the highest Chain Link. Each Card in the Chain is then resolved until Chain Link 1 resolves. Cards and Effects cannot be activated while the Chain is resolving.
Once the entire Chain resolves, if any Cards have not yet been moved to another location, they will be sent to the Graveyard. (This is considered to happen simultaneously with the last part of the resolution of Chain Link 1).
Player 1 activates "Raigeki" (Chain Link 1)
Player 2 activates "Imperial Order" in response to "Raigeki" (Chain Link 2)
Player 1 activates "Dark Bribe" in response to "Imperial Order" (Chain Link 3)
The Chain is resolved backwards, starting with the last Card that was activated.
(Chain Link 3) "Dark Bribe" negates the activation of "Imperial Order" and destroys it.
(Chain Link 2) "Imperial Order" has its activation negated, so nothing happens at this Chain Link.
(Chain Link 1) The Effect of "Raigeki" resolves, destroying all Monsters Player 2 controls.
The Chain ends with the remaining Cards ("Dark Bribe" and "Raigeki") sent to the Graveyard. (For timing purposes, this is considered to be done at the same time as the Effect of "Raigeki" destroying all of Player 2's Monsters.)