Does Overzealous Fan target an enemy unit, can Not So Fast counter it, and if so, does the Fan die?

Ruling: Overzealous Fan does target an enemy unit because the targeting is part of the effect, not the cost. Not So Fast can counter it. When countered, the Fan does not die because the whole ability is countered and the instruction (including the cost within instruction to kill the Fan) is not executed.

Sequence:

• Player B attacks into Player A who has Fan and another unit at the battlefield
• Initial chain happens, Fan's trigger is added to the chain targeting an enemy unit
• Not So Fast is played as a reaction targeting Fan's trigger
• Reactions may happen
• Not So Fast resolves, countering Fan's trigger
• Since the effect won't resolve, Fan won't die

Nuances:

• The cost to kill the Fan is a "cost within instruction" that is paid when the instruction executes, not a cost to put the ability on the chain
• Triggered abilities don't currently have printed costs in the traditional sense
• Costs within instructions are executed during resolution, so countering the ability prevents the cost from being paid