In a large skillet, brown chicken in oil. Stir in the tomatoes, onion, cumin, salt and cayenne. Bring to a boil. Reduce heat to low; cover and cook for 25-30 minutes or until a thermometer inserted in chicken reads 180°, stirring occasionally.
Remove chicken. When cool enough to handle, remove meat from bones; discard bones. Shred meat with two forks; return to skillet. Bring to a boil. Reduce heat; simmer, uncovered, for 8-10 minutes or until sauce is thickened.
Peel and cut avocado into slices; drizzle with lime juice. Spoon 1/2 cup chicken mixture over each tortilla. Top with avocado and if desired, cilantro and roll up.
