Arena Chips are a currency used to purchase Arena Crystals. They can be earned from Away Missions, and they were awarded in Arenas, but have been replaced with whole Arena Crystals.
Arena Chips originally had more uses; they were described as being able to unlock new arenas, but this mechanic was either dropped or never came to be. They could be donated to an Alliance Treasury for Alliance Missions, but it was later disabled before the Treasury was eventually removed altogether.
As of v6.0, Arena Chips have been completely removed. They were replaced with Arena Crystals in Away Missions.