It is the next discard phase after you "equip" it. So you take the action, you untap and you are ready to block this nasty Gangrel If the effect activated when you burn the card, it would be written. See for example superior Form of Corruption:
Form of Corruption
Action
Serpentis
Put this card in play. When your prey gets the Edge anew, put a counter on this card. During your master phase, if the number of counters on this card equals or exceeds the amount of blood on a vampire controlled by your prey, you may burn this card to take control of that vampire. A Methuselah can have only one Form of Corruption in play.
As above, and your prey burns 1 pool when you burn this card.
> Non-existant user wrote:
> It is the next discard phase after you "equip" it. So you take the action, you untap and you are ready to block this nasty Gangrel
>
Correct. The vampire untaps because the action was successful.
Name: Chill of Oblivion
[BH:R, LotN:PG]
Cardtype: Action
Discipline: Necromancy
+1 stealth action.
[nec] Put this card on a ready vampire. This vampire may burn this card in combat to treat aggravated damage as normal for the remainder of combat. A vampire can have only one Chill of Oblivion.
[NEC] As above, and this acting vampire untaps during your next discard phase.
Artist: Drew Tucker