From Bulbapedia, the community-driven Pokémon encyclopedia.
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Chain breeding is the process of breeding a move to a Pokémon that can only learn it as an Egg Move, then in turn using that Pokémon to pass down the move to another Pokémon that can learn the move as an Egg Move, but cannot breed with the original Pokémon.
Many breeding chains, however, are far longer than the Wish chain, and breeding chains can get longer still if a specific set of four moves is wanted on a specific Pokémon. Most chains that begin in the Field Egg Group are made easier by Smeargle's ability to learn any move through Sketch, and some, especially in early generations, explicitly require that a Smeargle Sketch a move that is otherwise exclusive to an all-female or genderless species, such as Heal Bell in Generation II exclusive to Miltank and Celebi or Lovely Kiss exclusive to Jynx.
Many moves must be chain bred, with these moves being more prevalent in earlier generations, as more Pokémon with larger learnsets and different Egg Group combinations continue to be introduced. What follows is a list of the steps needed to get an Eevee with Wish in Generation VIII from a male Togekiss through Pichu that needs to evolve into Pikachu to be able to breed: