In a medium bowl, combine 2 cups cooked chicken (shredded, sliced, or diced), 1 ripe avocado (diced or sliced), ½ cup cheddar or mozzarella cheese, ¼ cup sour-cream, mayo, or your favorite sauce, 2 Tablespoons chopped cilantro, and 1 Tablespoon lime or lemon juice. Gently toss until evenly mixed (fold carefully if avocado is sliced to avoid mashing).
Lay one large tortilla flat on a clean surface. Place about one-quarter of the filling mixture in the center of the tortilla in a line from near one edge toward the opposite edge.
Fold the sides of the tortilla in, then roll tightly from the filled edge to form a wrap. Repeat with the remaining tortillas and filling.
Heat a skillet or griddle over medium-high heat. Pour in 1 teaspoon oil and tilt the pan to coat the surface.
Place the wraps seam-side down in the hot pan (work in batches if they don't all fit without crowding). Cook 1–2 minutes until the bottom is golden, then flip and cook about 1 minute more until the other side is golden.
Remove the wraps from the pan, let rest briefly, slice if desired, and serve warm.