Mix the shredded chicken, cheese, avocado, sour cream, cilantro, and lime juice in a medium bowl.
Lay a tortilla flat on a flat surface and fill with some of the filling mixture. Wrap tightly to form a roll. Repeat the process for all tortillas.
Pour about 1 teaspoon oil into a heated pan or griddle. Place all four tortillas on the pan and cook for 1-2 minutes on medium-high heat. Flip on the other side and cook for another minute or until the burritos are golden in color. Serve warm.
Notes
Adjust the sauce to your preference for added flavor.