Arena of the Ages

The  is a colosseum which exists outside of time. It can be visited via a pillar at the End of Time in the Nintendo DS remake of Chrono Trigger.

In the Arena of Ages, time-travelers can breed monsters to do battle with one-another. The winners of these battles receive prizes. There are six different difficulties, but only three are available at a time. The higher the difficulty, the higher the price but you also get better prizes.