Lavalval Chain

2 Level 4 monsters
Once per turn: You can detach 1 Xyz Material from this card to activate 1 of the following effects:
● Send 1 card from your Deck to the Graveyard.
● Choose 1 Monster Card from your Deck and put it on top of your Deck.

When using the second effect, do i need to reveal the card?

Yes you must show it to your opponent to verify it's a Monster card.

Got it, thats all

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Situation

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1. I XYZ summon lavalval chain
2. Opp use BTH

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Question

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Can I use effect ?

Yeah, since it's your turn you have the right to priority. Lavalval Chain's ignition effect with be chain 1 and BTH will be chain 2. So Lavalval Chain will get removed then you use it's eff to ditch a card or put a monster on the top of your deck.

Also, since this comes down to a priority ruling;

http://yugioh.wikia.com/wiki/Priority
http://forum.duelingnetwork.com/t660-ruling-101-priority

technically, no, not after he activates BTH.
But then, he shouldn't have been able to activate BTH yet at that point, so the point is moot.
The opponent is supposed to verify that no ignition is going to be used with priority before responding, but most people don't bother on DN...