You can get your hands on Pikachu starting in Melemele Island's Route 1, an area very early in the game. Though, this Pokemon is a rare spawn that can take up hours of your time if you are unlucky. Because of this, it is recommended that you instead catch a Pichu, which is found in the same area, and evolve it into a Pikachu.
If you choose to go the evolution route, you will need to put in some effort to increase its happiness before it will evolve. To accomplish this, simply walk with Pichu in your party, use Pichu in combat, and equip a Soothe Bell (found in Route 3). Once you are successful in increasing its happiness to the required level, it will automatically evolve into a Pikachu on the next level up.
As an added note, to evolve Pikachu into a Raichu all you need to do is use a Thunder Stone. These are found in four different locations, one of which is in the jewelry shop of Konikoni City.
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