A chain is a sequence of card effects that react to one another OR activate simultaneously. I've gone through many of my rulings talking about "this can only chain to that" or "this happens in a chain", and etc.
There are certain rules however on how a chain is organized. Most of which concerns a monster's effect.
How are chains organized.
Chains are organized by Chain Link 1 being the first to activate, Chain Link 2 being the next, and so forth. After the sequence of card activating is done, this means neither player has a card they can use to continue the chain, meaning it is time to resolve. Resolving a chain starts with the last card to activate and continues working backwards from there.
Responding to an Activation.
This rule should be familiar with most of by now. When you decide to activate one card after another, that is a chain occurring.
Player 1: Activates Mirror Force
Player 2: Responds with Book of Moon and targets his/her monster.
Chain Link 2: Book of Moon
Chain Link 1: Mirror Force
Remember my Spell Speed Post? That post will tell you what card can chain to what and where it can happen on a chain.
How Do You Know If You Can't Chain To This Card Effect
Simultaneous Activation mostly occur for cards with Trigger Effects have their conditions fulfilled at the same time. There is certain way how a chain of Trigger Effects is organized.
In my Miss Timing Post and my Trigger Effect Post, I've talked about Mandatory Trigger Effects and Optional Trigger Effects, well in a chain Mandatory Trigger Effects always occur first in a chain and then any other Optional Trigger Effect.
Player 1 has Sangan and Botanical Girl on the Field.
Player 2 activates Dark Hole
(Sangan and Botanical Girl are destroyed and sent to the graveyard)
Chain Link 1: Sangan
Chain Link 2:Botanical Girl
If 2 or more Mandatory Trigger Effects are activated at the same time, you can choose which chain link it'll be in as long as its not after any Optional Trigger Effects. If a Mandatory Trigger Effect is suppose to activate during a chain, it'll start a new chain as chain link 1.
Player 1 has Mystical Space Typhoon set and Sangan on the field.
Player 2 has Raigeki Break set
(Supposing its been long enough for either players to activate their set facedowns.)
Player 1 activates Mystical Space Typhoon and targets Player 2's set card.
Player 2 chains Raigeki Break, discards 1 card and targets Sangan.
Chain Link 1: Mystical Space Typhoon
Chain Link 2: Raigeki Break
Chain Link 2: Raigeki Break destroys Sangan
Chain Link 1: Mystical Space Typhoon destroys Raigeki Break
(New Chain Link)
Chain Link 1: Sangan
If 2 or more Optional Trigger Effects are activated at the same time, you can choose which chain link it'll be in as long as its not before any Mandatory Trigger Effects. Unmissable Optional Trigger Effects are in the same league as Miss-able Trigger Effects.
During the End Phase, you can chain to a card effect with any of your card that have a legal activation, however cards with "If this card is...., at the End Phase...." in their text, do not chain to each other during End Phase. They will activate in their own Chain Link as chain link 1, independent from other card effects occurring at that point. However you can choose what card effect can occur first and last such as a normal chain.
A Couple Cards in this category are like T.G's and Stardust Dragon.