Walkthrough
While on Route 22, you will run into your Rival and he will challenge you to another battle. He has been training since your last battle with him, even adding another Pokemon to his Party. This battle against your Rival is optional, being available until after you have earned your first Gym Badge. Unlike in Pokemon Yellow, this battle has so significance on your Rival's Team later in the game, so you don't need to head to Route 22 if you don't want to do this battle. Your Rival should be easy to defeat once again, but you can always catch a Pikachu in Viridian Forest if you're having trouble with his Pidgey.
Rival (Bulbasaur Chosen): Level 9 Pidgey, Level 9 Charmander
Rival (Charmander Chosen): Level 9 Pidgey, Level 9 Squirtle