1. Breed a Pikachu: Pichu is the baby form of Pikachu. To get one, you'll need to breed two Pikachu that have the "Cute Charm" ability. This increases the chance of a baby Pokémon being born.
2. Trade: You can trade for a Pichu from someone who has already bred one. This is probably the easiest way to get a Pichu in HeartGold.
Remember, breeding and trading are the only ways to get a Pichu in Pokémon HeartGold.