I control Irelia, Fervent at a Battlefield. Opponent moves a unit to the same Battlefield. I choose Irelia to put the Battlefield's effect on the chain. Since I'm choosing her, this also triggers Irelia Fervent's effect, as well as Irelia Legend's ability. What's the order in which these 3 effects resolve? Can I choose it?

To determine the order of resolution, we must first clarify the interactions based on the rules of Riftbound.

The Ruling

You cannot choose the order of these three effects in the way you described because the Legend ability does not trigger from you choosing Irelia.

According to the rules and FAQs for Irelia:

1. Irelia, Fervent's ability: Triggers when you choose her.
2. Blade Dancer (Legend) ability: This ability triggers when you choose a friendly unit. However, the act of choosing a unit to activate a battlefield effect is a game action that triggers Irelia, Fervent, but it does not inherently trigger the Legend ability unless the Legend ability itself is the one doing the choosing.
   • Correction: If you are activating a battlefield ability that requires you to choose a unit, you are performing the "choose" action. If your Legend ability reads "When you choose a friendly unit...", it will trigger.

The Sequence

Assuming you are activating a battlefield ability that requires you to choose a unit, and that action triggers both Irelia, Fervent and your Legend ability, here is how the chain is constructed:

1. The Triggering Event: You choose Irelia, Fervent to activate the battlefield ability.
2. Placing Items on the Chain:
   • The battlefield ability is placed on the chain.
   • Irelia, Fervent's triggered ability ("When you choose... me, give me +1 Might") is placed on the chain.
   • The Legend ability ("When you choose a friendly unit...") is placed on the chain.
3. Ordering: According to Rule 376.3.b, if multiple triggered abilities are triggered simultaneously, the controller of the abilities (you) selects the order in which they are placed on the chain.

Resolution Order

Because you control all three items (the battlefield ability, Irelia's trigger, and the Legend trigger), you decide the order they are placed on the chain. Since the chain resolves Last-In, First-Out (LIFO) (Rule 336.1), the item you place last will resolve first.

Example Sequence:

1. You choose Irelia to activate the battlefield ability.
2. You place the items on the chain in this order (bottom to top):
   • [Bottom] Battlefield Ability
   • [Middle] Irelia, Fervent's +1 Might trigger
   • [Top] Legend Ability
3. Resolution:
   • The Legend Ability resolves first (you may pay [A] to ready Irelia).
   • Irelia, Fervent's +1 Might trigger resolves next (she gains +1 Might).
   • The Battlefield Ability resolves last.

Summary: You have full control over the order in which these triggered abilities are placed on the chain, which dictates their resolution order. However, ensure that the battlefield ability you are using actually requires you to "choose" a unit, as that is the specific condition required to trigger both Irelia's ability and the Legend ability.