The Chain Lightning spell doesn't show a buff in the Status of the Hero. Most buffs that show in the status are from aura abilities, so you need to base your spell from an aura ability to make the buff appear at the status.
you set the duration to ZERO. it will be permanent unless you will cast a spell to the targeted unit.
have you even tried adding a buff to a chain lightning based spell? as we said, buff will never show if the base spell doesn't use a buff by default...
@Arhowk - btw, there is a chain spell system at the spells section...