Pichu wasn't introduced to the Pokemon world until Pokemon Gold and Silver (which came before Crystal). In these games, Pichu is a very rare encounter that can be found in Ilex Forest and Dark Cave.
Here's the catch: You can only catch Pichu if you encounter a wild Pikachu and it holds a Light Ball. A Pikachu holding a Light Ball has a chance of evolving into a Pichu instead of a Raichu.
While Pichu isn't available in Crystal, you can encounter Pikachu in Goldenrod City's Game Corner (using the slot machines) or by battling Whitney in Goldenrod City's Gym.