The effect that places 1 Counter onto “Colosseum – Cage of the Gladiator Beasts” whenever a monster is Special Summoned from a player’s Deck begins a Chain.
Discarding 1 card to prevent “Colosseum – Cage of the Gladiator Beasts” from being destroyed by a card effect does not use the Chain. You discard the 1 card when resolving the effect that should destroy “Colosseum – Cage of the Gladiator Beasts”.