If your opponent activates and you chain Tools of the must discard a card even though was negated?

You are correct! If your opponent activates a card and you chain Tools of the Trade to negate it, you still have to discard a card.

Here's why:

* Tools of the Trade has a cost, not a requirement. It says, "Discard 1 card; negate the activation..." This means you must discard a card as part of the cost to activate the effect, regardless of whether or not the card you're negating resolves.

* Negation only stops the card from resolving. It doesn't retroactively erase the fact that you activated Tools of the Trade.

Therefore, even though your opponent's card was negated, you still have to discard a card as the cost of using Tools of the Trade.