The Chocobo Egg can first be acquired in Crustacia. A Mad Monk there will offer to sell the player an Amulet of Annihilation for 10,000 Jewels. If the player purchases it and does not currently own the Chocobo Egg, the Mad Monk will give them the Chocobo Egg in addition to their purchase.
Finally, a trader in Ivor Tower Alley will trade the egg for 9 Spice and 9 Perfume. The player must make this trade before fighting Mungola, as the alley closers and the traders cannot be accessed after Mungola's defeat.
The Chocobo Egg in turn can be traded for the Magic Gourd in Nobilia Marketplace. This is a pointless trade as the Gourd does nothing, but the player can do the trade and then re-acquire the Chocobo Egg elsewhere if they wish to acquire all Charms.