The Emblem Choice Chest is an item that can be used to receive Faction Emblems of your choice.
Faction Emblems are the rarest Emblems, and acquiring them will be harder than Primordial Emblems or Amplifying Emblems. The best source of Faction Emblems are Emblem Choice Chests from which you can choose which emblems you want to obtain.
Emblem Choice Chests are mainly obtained from events. They can also be obtained from currently ongoing Tavern Bargains event (as an Emblem Choice Chest), Towers of Esperia quest from floors 200+, gift sets, and AFK Rewards starting from Chapter 19. They can be also bought from the Store or Arcane Labyrinth for Diamonds.