If Kinkou Monk is the only friendly unit on the board (or only one other friendly unit exists), can its triggered ability activate to buff that single unit, or does it require two valid targets to activate at all?

Ruling: Kinkou Monk's triggered ability requires two valid targets (two other friendly units) to be placed on the chain. If only one or zero other friendly units are available when the ability would trigger, the ability cannot be activated at all and fails to enter the chain.

Sequence:

• When Kinkou Monk is played, its triggered ability attempts to activate
• During the targeting step (559.3), you must choose two other friendly units as required by the card text
• If fewer than two valid targets exist, you cannot complete the targeting requirement
• The legality check (562.3) determines the action is illegal due to insufficient valid targets
• The ability activation is cancelled and never enters the chain

Nuances:

• This is different from a target becoming invalid after the ability is on the chain - in that case, the ability still resolves and buffs any remaining valid targets ("do as much as you can")
• Cards with "up to" wording (like "up to two units") allow choosing fewer targets, but Kinkou Monk lacks this optional language
• The distinction between "must have valid targets to activate" versus "resolve as much as possible" is key: the former applies when putting abilities on the chain, the latter when resolving them
• An already-buffed unit is still a valid target when choosing, though it won't receive another buff on resolution (unless it's Lee Sin's Calm or the buff was consumed)